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Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n=3–5). In all three FAMEs, the lowest energy conformer has a simple ‘all-trans’ structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the ‘extra’ bands that were observed in the Raman data but were not predicted for the all-trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-31G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-31G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data.This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-31G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.

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... This requires the quantitative experimental determination of, at least, relative intensities in the gas phase and a reliable relationship between theoretical and experimental intensities. These two requirements are currently met more robustly and frequently by infrared spectroscopy than by Raman spectroscopy [5][6][7]. However, Raman spectroscopy is typically more powerful in terms of spectral coverage and conformational resolution, due to the accessibility of low-frequency vibrations and the frequent occurrence of sharp Q-branch transitions. ...

... These insights are then used to quantify the conformational experimental intensities. These two requirements are currently met more robustly and 24 frequently by infrared spectroscopy than by Raman spectroscopy [5][6][7]. However, Raman 25 spectroscopy is typically more powerful in terms of spectral coverage and conforma- 26 tional resolution, due to the accessibility of low frequency vibrations and the frequent 27 occurrence of sharp Q-branch transitions. ...

... In the chosen example, it is difficult to judge whether conformer 1 or conformer 2 is more dominant in the jet expansion, due to the spectral overlap and the theoretical intensity error. A similar observation has been reported for the Raman spectrum of liquid and solid methyl butanoate [6]. The computational models that were feasible almost 20 years ago profited from systematic anharmonic shifts and allowed for the qualitative assignment of conformers, but the calculated Raman intensities were too erratic for any quantitative analysis. ...

The conformational preferences of the ester group have the potential to facilitate the large amplitude folding of long alkyl chains in the gas phase. They are monitored by Raman spectroscopy in supersonic jet expansions for the model system methyl butanoate, after establishing a quantitative relationship with quantum–chemical predictions for methyl methanoate. This requires a careful analysis of experimental details, and a simulation of the rovibrational contours for near-symmetric top molecules. The technique is shown to be complementary to microwave spectroscopy in quantifying coexisting conformations. It confirms that a C−O−C(=O)−C−C chain segment can be collapsed into a single all-trans conformation by collisional cooling, whereas alkyl chain isomerism beyond this five-membered chain largely survives the jet expansion. This sets the stage for the investigation of linear alkyl alkanoates in terms of dispersion-induced stretched-chain to hairpin transitions by Raman spectroscopy.

... experimental intensities. These two requirements are currently met more robustly and 24 frequently by infrared spectroscopy than by Raman spectroscopy [5][6][7]. However, Raman 25 spectroscopy is typically more powerful in terms of spectral coverage and conforma- 26 tional resolution, due to the accessibility of low frequency vibrations and the frequent 27 occurrence of sharp Q-branch transitions. ...

... ESI of Ref. [13]. In order to account for this, it would be necessary to multiply the parallel The quantum efficiency of a CCD camera is dependent on the wavelength of the 231 absorbed light, which has the potential to significantly distort recorded intensities [6]. ...

... A complete torsional scan of the B2PLYP-D3(BJ)/aug-cc-pVTZ PES has already 565 been performed [9]. In this work, only the stationary points were recalculated at the barriers of interconversion are shown in Figure 9 and in Table 4, including a pioneering 568 DFT study [6]. The implications for the experiment shall be briefly discussed here. ...

The conformational preferences of the ester group have the potential to facilitate the large amplitude folding of long alkyl chains in the gas phase. They are monitored by Raman spectroscopy in supersonic jet expansions for the model system methyl butanoate, after establishing a quantitative relationship to quantum-chemical predictions for methyl methanoate. This requires a careful analysis of experimental details, and a simulation of the rovibrational contours for near-symmetric top molecules. The technique is shown to be complementary to microwave spectroscopy in quantifying coexisting conformations. It confirms that a C-O-C(=O)-C-C chain segment can be collapsed into a single all-trans conformation by collisional cooling, whereas alkyl chain isomerism beyond this five-membered chain largely survives the jet expansion. This sets the stage for the investigation of linear alkyl alkanoates in terms of dispersion-induced stretched-chain to hairpin transitions by Raman spectroscopy.

... Thus, polymer chains are simulated by short segments capable of reproducing the chemical environment in terms of interaction sites and steric hindrance around them. Furthermore, molecular models containing aliphatic chains and multiple conformational degrees of freedom, such as aliphatic esters or amides, are known to exhibit shallow Potential Energy Surfaces (PES) [275,276]. A preliminary PES exploration to identify relevant stationary state(s) is a fundamental step in the structure-optimization strategy because any ab-initio method will invariably localize the minimum that is closer to the initial input geometry. ...

... The maximum ΔG value for homogeneous nucleation is obtained by substituting Eq. (277) into Eq. (276), resulting in the following key equation: ...

... From the above exposition and Eqs. (276)(277)(278)(279), it is clear that application of the nucleation theory requires a sufficiently accurate estimation of the dissolved amount of fluid (foaming agent) in the polymer matrix, and also the estimation of the induced plasticization of the polymer matrix, of the interfacial tension between the gas nuclei and the polymer phase, as well as of the chemical potentials of all components in the metastable polymer and nucleating phases. As mentioned already, NRHB model can be of much assistance here. ...

Understanding and predicting sorption thermodynamics of low molecular weight compounds in rubbery and glassy polymers is of great relevance to elucidate important phenomena in areas at the interface of various scientific branches, such as the colloid and interface science, membrane science, polymer foaming, tissue engineering, scaffolding, microcellular materials, aerogels, and for the implementation of technological applications. The development of thermodynamic models for polymer-based mixtures, applicable over a wide range of conditions, remains an active and fascinating research area. Recent advances in statistical thermodynamics and a better understanding of intra- and inter-molecular interactions, thanks to accurate experimental measurements and molecular simulations using realistic force fields, have contributed significantly to this end. In fact, sorption thermodynamics in polymers plays a relevant role in describing phase equilibria of polymer mixtures, (hydro)gel swelling, intramolecular association, hydrogen-bonding cooperativity and polymer degradation and stability, in assessing durability of polymers exposed to aggressive environments, in predicting penetrant induced crystallization and plasticization phenomena in polymers, in designing polymer-based separation processes, in tailoring polymer foaming processes, in improving gas and vapor barrier properties of polymer packaging, in modelling devolatilization of polymer solutions and migration phenomena of additives, in designing drug delivery systems, to mention a few.
In the last decades, models have been introduced rooted on Equation of State theories, some of them based on compressible lattice frameworks. Notably, these models have been structured to specifically account for non-random distribution of molecular species and for dealing with several kinds of self-interactions that establish between polymer molecules and between penetrant molecules as well as cross-interactions that establish between moieties present on polymer backbone and penetrants. These models have been built to describe the behaviour of both rubbery polymers and out-of-equilibrium glassy polymers. Towards the further development of these approaches to gain an increased predictive capability of this thermodynamic description, recently have been also introduced approaches aimed at the estimation of relevant parameters based on molecular descriptors for calculations of properties of pure-components bulk phases and solutions.
Such a quantitative description of the sorption process by use of advanced thermodynamic theories invariably relies on a molecular-level characterization of the system under scrutiny to validate and support the theoretical framework. Information is required on the molecular aggregates formed in the system, their structure, stoichiometry and, whenever possible, their population. In this respect, vibrational spectroscopy (FTIR, Raman) has demonstrated to be among the most powerful techniques, due to its sensitivity towards H-bonding detection and to its sampling flexibility, which allows the development of in-situ, time-resolved measurements. In the last ten years, significant advancements have occurred in terms of both experimental approaches and data analysis techniques, which considerably contributed to deepening the interpretation of the molecular interactions scenario. In particular, Two-dimensional correlation spectroscopy (2D-COS), Difference spectroscopy (DS) and first-principles quantum chemistry calculations have made a strong impact on the amount and quality of the acquired information.
In view of the progress in this rapidly advancing and technologically relevant subject, this review article summarizes the state of the art on sorption thermodynamics modelling and on synergic combination with the wealth of information recently made available thanks to advanced vibrational spectroscopy techniques.

... A conformer is accepted, with a probability defined by the Metropolis criterion, only if there are no overlapping atoms. Rotating bonds comprise the CO À C2 (c 0 ) and all the CH 2 À CH 2 (c i , i = 1,2,3, ..) bonds; the CH 3 À O À C=O dihedral angle was kept in the cis state (C=O and OÀCH 3 coplanar and on the same side), because the other configuration (C= O and OÀCH 3 coplanar and on opposite sides) was reported to be more than 30 kJ mol À1 higher in energy.333435 Thus, the total number of rotating bonds (Nb) is equal to 12 for methyl myristate, 14 for palmitate and 16 for stearate. ...

... Thus, the total number of rotating bonds (Nb) is equal to 12 for methyl myristate, 14 for palmitate and 16 for stearate. For the each rotating bond, three states were considered, with dihedral angles equal to 1808 (trans or t) and AE 658 (gauche AE or g AE), [33, 36] as shown inFigure 2. The torsional potential of each conformer (J) was calculated as the sum of single bond contributions, Equation (7) in which DV i gt is the gauche/trans energy difference for the ith bond and n i J = 1 orFigure 2. Newman projection of the trans (left) and the gauche + (right) states of a bond; the gaucheÀ state differs from gauche + state by the sign of the rotation. For the COÀCH 2 bond, the CH 3 O-CO-CH 2 -CH 2 dihedral angle is measured. ...

... Whereas there is little uncertainty for the energetic parameters of alkyl chain bonds, [37] less is known about the COÀCH 2 bond and the adjacent CH 2 ÀCH 2 bond. From DFT calculations for methyl propionate, gauche/trans energy differences higher than 3 kJ mol À1 were obtained for the CO À CH 2 bond (c 0 ), [34, 35] whereas the energy of methyl butyrate was found to be slightly affected by rotations of the CH 2 À CH 2 bond (c 1 ). [33] We used the values DV o gt = 3.5 kJ mol À1 and DV i gt = 2.2 kJ mol À1 for i = 3, 4,… NbÀ1. For simplicity we assumed DV 1 gt = 0 and also DV 2 gt = 0 was used, which provided good agreement between calculated and measured quadrupolar splittings. ...

Insensitive towards inversion: Can residual dipolar couplings (RDCs) and other anisotropic NMR observables be used to determine absolute configuration? A critical assessment of recent approaches is provided to determine the absolute configuration from RDCs.

... Rotating bonds comprise the CO À C2 (c 0 ) and all the CH 2 À CH 2 (c i , i = 1,2,3, ..) bonds; the CH 3 À O À C=O dihedral angle was kept in the cis state (C=O and OÀCH 3 coplanar and on the same side), because the other configuration (C= O and OÀCH 3 coplanar and on opposite sides) was reported to be more than 30 kJ mol À1 higher in energy. [33][34][35] Thus, the total number of rotating bonds (Nb) is equal to 12 for methyl myristate, 14 for palmitate and 16 for stearate. For the each rotating bond, three states were considered, with dihedral angles equal to 1808 (trans or t) and AE 658 (gauche AE or g AE), [33,36] as shown in Figure 2. The torsional potential of each conformer (J) was calculated as the sum of single bond contributions, Equation (7) in which DV i gt is the gauche/trans energy difference for the ith bond and n i J = 1 or n i J = 0, according to whether the ith bond is in the gauche or in the trans state. ...

... [33][34][35] Thus, the total number of rotating bonds (Nb) is equal to 12 for methyl myristate, 14 for palmitate and 16 for stearate. For the each rotating bond, three states were considered, with dihedral angles equal to 1808 (trans or t) and AE 658 (gauche AE or g AE), [33,36] as shown in Figure 2. The torsional potential of each conformer (J) was calculated as the sum of single bond contributions, Equation (7) in which DV i gt is the gauche/trans energy difference for the ith bond and n i J = 1 or n i J = 0, according to whether the ith bond is in the gauche or in the trans state. ...

... From DFT calculations for methyl propionate, gauche/trans energy differences higher than 3 kJ mol À1 were obtained for the CO À CH 2 bond (c 0 ), [34,35] whereas the energy of methyl butyrate was found to be slightly affected by rotations of the CH 2 À CH 2 bond (c 1 ). [33] We used the values DV o gt = 3.5 kJ mol À1 and DV i gt = 2.2 kJ mol À1 for i = 3, 4,… NbÀ1. For simplicity we assumed DV 1 gt = 0 and also DV 2 gt = 0 was used, which provided good agreement between calculated and measured quadrupolar splittings. ...

The overall and detailed elucidation (including the stereochemical aspects) of enzymatic mechanisms requires the access to all reliable information related to the natural isotopic fractionation of both precursors and products. Natural abundance deuterium (NAD) 2D-NMR experiments in polypeptide liquid-crystalline solutions are a new, suitable tool for analyzing site-specific deuterium isotopic distribution profiles. Here this method is utilized for analyzing saturated C14 to C18 fatty acid methyl esters (FAMEs), which are challenging because of the crowding of signals in a narrow spectral region. Experiments in achiral and chiral oriented solutions were performed. The spectral analysis is supplemented by the theoretical prediction of quadrupolar splittings as a function of the geometry and flexibility of FAMEs, based on a novel computational methodology. This allows us to confirm the spectral assignments, while providing insights into the mechanism of solute ordering in liquid-crystalline polypeptide solutions. This is found to be dominated by steric repulsions between FAMEs and polypeptides.

... Theoretical studies of lipids compounds has been performed in order to establish the general rules which govern the relative energies of the conformers in short-chain FAME [26]. Density functional calculations have been used to investigate the conformations and Raman spectra of long-chain FAME [27]. Properties such as chain length and degree of unsaturation were determined. ...

... Fig. 2 shows the Raman spectra for the main esters present in soybean biodiesel, as listed in Table 1, plus the (12:0) and (14:0), which are references for the analysis of unsaturated esters in the liquid phase. Differences are observed in the Raman intensities and frequencies of some bands due to several factors, including: liquid vs. solid phases [16,25], number of carbon atoms in the chains [16,26,27] and number of insaturations [16]. The line shape of a biodiesel Raman spectrum is determined by the relative amount of these esters. ...

This work provides a systematic and comprehensible lineshape analysis of the Raman spectra from (i) the main esters that compose the soybean biodiesel, namely Palmitate, Stearate, Oleate, Linoleate and Linol- enate, (ii) mixtures of these esters, (iii) a soybean biodiesel reference material. Using theoretical spectral simulation as a guide, the experimental spectra are fit considering all the 3N-6 vibrational modes, where N is the number of atoms in the molecule. We demonstrate that while intensity analysis may lead to uncertainty in the definition of the relative ester contents in a mixture, a complete spectral analysis involving all parameters, including peak frequencies, allows spectral determination of esters composi- tion. Finally we define a protocol that can be used for defining the specific composition of unknown, including adulterated biodiesels, important for quality control.

... These structures still required further optimization. Next, we used the B3LYP/6-31G(d) [39,40] method and basis set for all optimization and frequency calculations. The lowest energy structures were now located. ...

This paper reports the computational study of phosphorus-doped boron clusters PBn/PB–n/PB+n (n = 4–8). First, a global search and optimization of these clusters were performed to determine the stable structures. We used density functional theory (DFT) methods and ab initio calculations to study the stability of the atomic clusters and to explore the arrangement of stable structures. We found that the lowest energy structures of the smaller phosphorus-doped boron clusters tend to form planar or quasi-planar structures. As additional boron atoms are added to the smallest structures, the boron atoms expand in a zigzag arrangement or in a net-like manner, and the phosphorus atom is arranged on the periphery. For larger structures with seven or eight boron atoms, an unusual umbrella-like structure appears. We calculated the binding energy as well as other energies to study cluster stability. We calculated the ionization energy, electron affinity, and the HOMO–LUMO gaps. In addition, we used the adaptive natural density partitioning program to perform bond analysis so that we have a comprehensive understanding of the bonding. In order to have a suitable connection with the experiment, we simulated the infrared and photoelectron spectra.

... To improve the initial proposed CK structures, we used the HF/STO-3G method. In order to obtain reliable and stable structures, we then used density functional theory (DFT) with the B3LYP [16,17] functional and the 6-31G(d) [18] basis set to re-optimize the structures. We then calculated the frequencies to confirm that the structures had no virtual frequencies. ...

We report a comprehensive theoretical investigation on phosphorus–boron mixed neutral, anionic, and cationic clusters P2Bn/P2Bn−/P2Bn+ (n = 3–7) with two phosphorus atoms and three to seven boron atoms. We reveal the common character of all the structures (i.e., the phosphorus atoms choose to occupy the peripheral position), whereas the boron atoms tend to be in the central and inside position of the ground state phosphorus—boron mixed clusters at each stoichiometry. Any three atoms preferentially form a stable triangle and grow with zigzag shape in a planar network. Interestingly, a series of planar motifs (including tetra-, penta-, and hexa-coordination) have been discovered in the phosphorus–boron clusters. The large binding energies (3.6 to 4.6 eV/atom) and quite large HOMO–LUMO gaps (5 to 10 eV) indicate the high stability of the clusters. The energy differences Δ1E, Δ2E, and energy gaps display oscillating behavior with increasing numbers of boron atoms. The electron affinity (EA) and ionization potential (IP) generally have small variations, with the EA values ranging from 2 to 3 eV, and the IP values ranging from 7 to 9 eV. Chemical bond analysis shows that the existence of multi-center delocalized bonds stabilize the clusters.

... Their peaks form well behaved trends and are relatively well separated and comprehensively understood as described by a body of published work on using Raman spectra for the analysis of fatty acids. [9][10][11][12][13][14] A code version of calculating PCA is presented which has been developed for understanding rather than computation speed and is freely available to support the reader in undertaking their own explorations. ...

Spectroscopy rapidly captures a large amount of data that is not directly interpretable. Principal Components Analysis (PCA) is widely used to simplify complex spectral datasets into comprehensible information by identifying recurring patterns in the data with minimal loss of information. The linear algebra underpinning PCA is not well understood by many applied analytical scientists and spectroscopists who use PCA. The meaning of features identified through PCA are often unclear.
This manuscript traces the journey of the spectra themselves through the operations behind PCA, with each step illustrated by simulated spectra. PCA relies solely on the information within the spectra, consequently the mathematical model is dependent on the nature of the data itself. The direct links between model and spectra allow concrete spectroscopic explanation of PCA, such the scores representing âconcentrationâ or âweightsâ. The principal components (loadings) are by definition hidden, repeated and uncorrelated spectral shapes that linearly combine to generate the observed spectra. They can be visualized as subtraction spectra between extreme differences within the dataset. Each PC is shown to be a successive refinement of the estimated spectra, improving the fit between PC reconstructed data and the original data. Understanding the data-led development of a PCA model shows how to interpret application specific chemical meaning of the PCA loadings and how to analyze scores.
A critical benefit of PCA is its simplicity and the succinctness of its description of a dataset, making it powerful and flexible.

Anthraquinones are a family of natural products with useful bioactivity and optical properties. An anthraquinone called parietin is produced by extremophiles to protect against solar ultraviolet B radiation, so it is a potential biosignature in astrobiology. Raman spectroscopy, which is now used in space environments, can detect molecules such as parietin based on molecular vibrations. In this study, we show that time-dependent density functional theory (TDDFT) can accurately calculate the Raman spectra of three dihydroxyanthraquinones: parietin, emodin, and chrysophanol. By comparing calculated spectra to measured Raman spectra from purified powders, 10 vibrational modes are identified. The detailed molecular motions of these fused ring vibrations are described, and vibrations modes that are common to all three molecules are highlighted. In addition to powder spectra, Raman measurements from the thallus of Xanthoria parietina, a lichen that produces parietin, are reported, with excellent agreement to both the parietin powder and calculated Raman spectra. These results show that TDDFT calculations could make significant contributions to spectral analysis in the search for biotic organic materials beyond Earth.

The denitrification of low-temperature flue gas is a difficult problem facing the industry. OH radicals can effectually oxidize NO in flue gas, which can achieve denitrification of low-temperature flue gas. Heterogeneous Fenton reaction is an important method for the formation of OH radicals. A four-step reaction mechanism of the formation of OH radicals by heterogeneous Fenton reaction is proposed and investigated in this paper. Theoretical results show that activation energy of the formation of OH radicals catalyzed by ZSM5-Si/Fe is much lower than that without catalyst. After doping Al/Ce/Ti, the activation energy is further reduced significantly. The activity is related to the active center atom of the catalyst. By comparing, ZSM5-Ce/Al–Fe has better catalytic performance because of its more fluffy structure. This study would provide an important theoretical reference for the design of the catalysts in heterogeneous Fenton reaction and their industrial applications.

Surface-enhanced Raman scattering (SERS) spectra contain information on the chemical structure on nanoparticle surfaces through the position and alignment of molecules with the electromagnetic near field. Time-dependent density functional theory (TDDFT) can provide the Raman tensors needed for a detailed interpretation of SERS spectra. Here, the impact of molecular conformations on SERS spectra is considered. TDDFT calculations of the surfactant cetyltrimethylammonium bromide with five conformers produced more accurate unenhanced Raman spectra than a simple all-trans structure. The calculations and measurements also demonstrated a loss of structural information in the CH2/CH3 scissor vibration band at 1450 cm-1 in the SERS spectra. To study lipid bilayers, TDDFT calculations on conformers of methyl phosphorylcholine and cis-5-decene served as models for the symmetric choline stretch in the lipid headgroup and the C═C stretch in the acyl chains of 1,2-oleoyl-glycero-3-phosphocholine. Conformer considerations enabled a measurement of the distribution of double-bond orientations with an order parameter of SC═C = 0.53.

In the present study, a Raman line-imaging setup was employed to monitor in situ the CO2 sorption at elevated pressures (from 0.62 to 7.10 MPa) in molten PCL. The method allowed the quantitative measurement of gas concentration in both the time-resolved and the space-resolved modes. The combined experimental and theoretical approach allowed a molecular level characterization of the system. The dissolved CO2 was found to occupy a volume essentially coincident with its van der Waals volume and the estimated partial molar volume of the probe did not change with pressure. Lewis acid-Lewis base interactions with the PCL carbonyls was confirmed to be the main interaction mechanism. The geometry of the supramolecular complex and the preferential interaction site were controlled more by steric than electronic effects. On the basis of the indications emerging from Raman spectroscopy, an equation of state thermodynamic model for the PCL-CO2 system, based upon a compressible lattice fluid theory endowed with specific interactions, has been tailored to account for the interaction types detected spectroscopically. The predictions of the thermodynamic model in terms of molar volume of solution have been compared with available volumetric measurements while predictions for CO2 partial molar volume have been compared with the values estimated on the basis of Raman spectroscopy.

Solvate crystal structures serve as useful models for the molecular-level interactions within the diverse solvates present in liquid electrolytes. Although acyclic carbonate solvents are widely used for Li-ion battery electrolytes, only three solvate crystal structures with lithium salts are known for these and related solvents. The present work, therefore, reports six lithium salt solvate structures with dimethyl and diethyl carbonate: (DMC)2:LiPF6, (DMC)1:LiCF3SO3, (DMC)1/4:LiBF4, (DEC)2:LiClO4, (DEC)1:LiClO4 and (DEC)1:LiCF3SO3 and four with the structurally related methyl and ethyl acetate: (MA)2:LiClO4, (MA)1:LiBF4, (EA)1:LiClO4 and (EA)1:LiBF4.

A method to monitor endocrine-disrupting chemical contamination phthalate esters (PAEs) by surface-enhanced Raman scattering (SERS) spectroscopy has been investigated. The molecular structure and assignment of the vibrations of dimethyl phthalate (DMP), forming short chains in PAEs, has been studied by density functional theory (DFT) calculations. The structure of DMP with the dihedral angles of 1C-6C-11C-13O and 4C-5C-18C-20O being 133.78° and -24.00°, respectively, has the lowest energy. Theoretical vibrational frequencies using B3LYP/6-31+G(d) (after scaling) show excellent agreement with the experimental normal Raman spectrum. In the region 200-1800 cm−1, SERS spectra of DMP were measured using ordered gold nanosubstrates. All except the weak signals in the normal Raman spectrum of DMP were successfully enhanced. These results demonstrate that SERS technology could be developed as a rapid method for screening of DMP.

Sorption of water in PCL, with specific focus on the hydrogen bonding interactions, has been analysed by combining ab-initio calculations, macroscopic thermodynamics modelling and relevant features emerging from spectroscopic and gravimetric measurements. FTIR data, analyzed by Difference spectroscopy, Two-dimensional correlation spectroscopy and least-squared curve fitting analysis, associated with gravimetric determination of water sorption isotherm, provided information on the system's behaviour and on the molecular interactions established between the polymer and the penetrant. A consistent physical picture emerged pointing to the presence of two spectroscopically discernible water species (first-shell and second-shell layers), that have been quantified. Water molecules are present in the form of dimers within the polymer equilibrated with water vapour, up to a relative humidity of 0.65. At higher humidities clustering of water sorbed molecules starts to take place. The multi-component (OH) band representative of absorbed water has been interpreted with the aid of ab-initio calculations performed on suitably chosen model systems. The outcomes of spectroscopic analyses were interpreted at a macroscopic level by modeling the thermodynamics of water sorption in PCL based on a non-random compressible lattice theory accounting for Hydrogen Bonding (HB) interactions. Starting from the fitting of the gravimetric sorption isotherm, the model provided quantitative estimates for the amount of self- and cross-HBs' which compare favorably with the FTIR results.

Rotational barriers of PN bonds were studied under density functional theory using the B3LYP functional and two different basis sets to establish the electronic effect in them. These calculations were performed with toluene solvent interaction using the Polarizable Continuum Model to simulate the experimental conditions. The anomeric effect was established as an electronic effect that drives the PN rotational barriers. This effect is characterized by the highest chlorine substitution over the phosphorous atom using the NBO analysis, and the bond energy was calculated using a modified version of the bond energy change. The stabilization criterion was established by the normalized value of the bond energy. Additionally, intercross molecular orbital energies in rotational barriers were established as another criterion of conformation stabilization.

Extensive quantum chemistry (QC) modeling of new arsenic sulfides identified by TOF-MS was performed using Hartree–Fock and density functional calculations with the 6-311G∗ basis set and electronic energies as well as geometries of positively singly-charged mono-arsenic sulfide clusters were determined. It was found that the cyclic and bi-cyclic structures of AsSn+ (n = 1–7) clusters are more stable than open structures although all are hetero-cyclic. Also the structure of AsS7 is not the expected single ring AsS7 as analogous to the S8 molecule but it posses a double ring structure with arsenic atom three coordinated.

We have recently demonstrated that the second hyperpolarizability γ of a selected vibrational mode of a molecule can be determined by using the computational Raman activity against an internal standard with a known Raman γ value. This approach provides a convenient way for prediction of the γ magnitude of DOVE four wave mixing spectroscopy, an optical analogue to two-dimensional (2D) NMR. Here, by using the Hartree-Fock (HF) method, the density functional theory (DFT) method, and the second-order Møller-Plesset perturbation theory (MP2) method, we extend our early work from the less anharmonic region <2000 cm(-1) into the more anharmonic region >2000 cm(-1) covering C-H, C-D, and C≡N stretching modes of benzene, deuterated benzene, acetonitrile, deuterated acetonitrile, and tetrahydrofuran. The computed Raman γ values of these vibrational modes have been determined by using either the 992 cm(-1) Raman band of benzene or the compound's own Raman band (C-C stretch) around 800-1000 cm(-1) as an internal standard. In this more anharmonic region, the HF method with a larger basis set provides the best outputs and the predicted Raman γ values agree well with experimental values for most of the vibrational modes studied. By choosing a suitable method and basis set, this facile approach could be applied to a broader spectral range for Raman γ estimation of various materials.

In this paper, we describe the results of the intramolecular ketene–alkene [2+2] cycloaddition in 2-pent-4-enyl-octa-1,7-dien-1-one, at HF/6-31+G∗ and DFT-B3LYP/6-31+G∗ computational levels of theory. For this reaction, we have explored the four possible pathways at a supra-antara approach in which four possible products: 5-4-, and 6-4-membered fused [n.2.0] bicycle rings; 6-4-, and 7-4-membered fused [n.1.1] bicycle rings. In all cases, an asynchronous process was found with an appreciable interaction of the ketene central carbon with both carbons from the alkenes. We demonstrated that the reaction is driven towards the formation of 5-4 member rings instead of 6-4 member rings. In addition, the internal molecular orbital HOMO-2 was identified as the molecular orbital with higher nucleophilic reactivity.

Doubly vibrationally enhanced (DOVE) four-wave mixing spectroscopy, an optical analogue to 2D NMR, involves two infrared transitions and a Raman transition. The magnitude of the DOVE second hyperpolarizability γ (or third-order susceptibility χ((3))) can be theoretically estimated if the values of the dipolar moments of the two infrared transitions and the γ of the Raman transition are known. The Raman γ can be measured by using the four-wave mixing interferometric method or conventional Raman spectroscopy in the presence of an internal standard. In this work, we examine if one can use the Raman activity computed from density functional theory calculation to determine the Raman γ of selected vibrational modes of several samples including deuterated benzene, acetonitrile, tetrahydrofuran, and sodium benzoate aqueous solution. The 992 cm(-1) Raman band of benzene serves as an internal standard for organic solvents, and the 880 cm(-1) Raman band of hydrogen peroxide is for the aqueous solution sample with known γ values. We have found that the predicted Raman γ values from the computational Raman activities match experimental data reasonably well, suggesting a facile approach to predict the Raman γ of interested systems.

Indole-3-Aldehyde is a new organic non-linear material having good second harmonic generation. The optimized molecular geometry, harmonic vibrational frequencies, infrared intensities of Indole-3-Aldehyde (I3A, C(9)H(7)NO) in the ground state were carried out by using density functional theory (B3LYP) method with 6-31G(d,p) basis set. A detailed interpretation of the infrared spectrum of Indole-3-Aldehyde is reported. The vibrational frequencies are calculated and compared with experimental FT-IR spectra. The theoretical spectrograms of FT-IR of the title compound have been constructed in addition, theoretical information like ONIOM, potential energy surface, NBO, and Fukui function are also calculated. Unambiguous vibrational assignment of all the fundamentals was made using the potential energy distribution.

The resonance Raman spectra of ground and excited triplet states of the free base meso-tetraphenylporphyrin (H2TPP) were investigated. The density functional theory (DFT) calculations were carried out on both the states of the H2TPP and its isotopomers. The calculations provided predictions vibrational frequency shifts on excitation, which are more accurate than the absolute band positions because of cancellation of errors. The predicted shifts on excitation were typically small in the H2TPP molecules as the excitation was delocalized over the entire porphyrin ring system. It was observed that the interpretation of the resonance Raman spectra of the excited states of other tetrapyrroles using DFT calculation was viable.

High-quality surface-enhanced Raman scattering (SERS) spectra of aflatoxin (AF) B(1), B(2), G(1) and G(2) have been acquired using silver nanorod (AgNR) array substrates fabricated by oblique angle deposition method. Significant vibrational peaks are identified on the argon plasma-cleaned substrates, and those peaks agree very well with the Raman spectra calculated by density function theory (DFT). The concentration-dependent SERS detection is also explored. The relationship between the concentration (C) of different AFs and the SERS intensity (I) of the Raman peak at Δν = 1592 cm(-1) is found to follow the general relationship I = AC(α), with α ranging from 0.32 to 0.46 for the four AFs. The limits of detection (LODs) reach 5 × 10(-5) mol L(-1) for AFB(1), 1 × 10(-4) mol L(-1) for AFB(2), and 5 × 10(-6) mol L(-1) for both AFG(1) and AFG(2) in bulk solution, or 6.17 × 10(-16) mol/1.93 × 10(-4) ng of AFB(1), 1.23 × 10(-15) mol/3.88 × 10(-4) ng for AFB(2), 6.17 × 10(-17) mol/2.03 × 10(-5) ng for AFG(1), and 6.17 × 10(-17) mol/2.04 × 10(-5) ng for AFG(2) per laser spot. Principal component analysis (PCA) is used to successfully differentiate these four different kinds of AFs at different concentrations up to their detection limits. The LODs obtained from PCA agree with the LODs obtained by using peak fitting method. With such a low detection limit and outstanding differentiation ability, we prove the possibility of utilizing the SERS detection system as a platform for highly sensitive mycotoxin detection.

The vibrational properties of p-chloro-, p-methoxy- and p-nitrobenzohydroxamic acids (BHA) and of the unsubstituted BHA were investigated and the spectra were assigned. The assignment was made on the basis of the experimental information available about the Raman peaks of mono- and disubstituted benzenes and the procedure was greatly facilitated by the data obtained from high-level DFT quantum-chemical calculations. In order to support an intended assignment of the SER spectra of BHA on copper, the molecular electrostatic maps and Fukui functions were derived from ab initio calculations. Both quantum-chemical descriptors were shown to provide similar information about the possible BHA molecule–copper surface interaction sites. Copyright © 2003 John Wiley & Sons, Ltd.

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of a series of long-chain, saturated fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n=5–21) and two series of unsaturated FAMEs. The calculations showed that the lowest energy conformer within the saturated FAMEs is the simple (all-trans) structure and, in general, it was possible to reproduce experimental data using calculations on only the all-trans conformer. The only exception was C6H12O2, where a second low-lying conformer had to be included in order to correctly simulate the experimental Raman spectrum.The objective of the work was to provide theoretical justification for the methods that are commonly used to determine the properties of the fats and oils, such as chain length and degree of unsaturation, from experimental Raman data. Here it is shown that the calculations reproduce the trends and calibration curves that are found experimentally and also allow the reasons for the failure of what would appear to be rational measurements to be understood. This work shows that although the assumption that each FAME can simply be treated as a collection of functional groups can be justified in some cases, many of the vibrational modes are complex motions of large sections of the molecules and thus would not be expected to show simple linear trends with changes in structure, such as increasing chain length and/or unsaturation. Simple linear trends obtained from experimental data may thus arise from cancellation of opposing effects, rather than reflecting an underlying simplicity.

The accuracy of various computational methods (Hartree–Fock, MP2, CCSD, CAS-SCF, and several types of DFT) for predicting
relative intensities in Raman spectra for C6H6, C6D6, and C6F6 was compared. The predicted relative intensities for ν1 and ν2 were compared with relative intensities measured by an FT-Raman spectrometer. While none of these methods excelled at this
prediction, Hartree–Fock with a large basis set was most successful for C6H6 and C6D6, while PW91PW91 was the most successful for C6F6.

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.

The solvent dependence of the gelation properties, the thermotropic behavior, and the melting enthalpy of a series of enantiomerically pure cyclohexane-based bisamide and bisurea compounds are reported. The two series of gelators examined are related structurally with the intermolecular interactions responsible for gelation differing in a systematic manner through varying the length of the alkyl tail and the number of hydrogen bonding units present. The gelation properties of the compounds in decalin, DMSO, and 1-propanol were studied by FTIR spectroscopy and by comparison of the thermal stability of their gels as determined by dropping ball experiments and by differential scanning calorimetry (DSC). FTIR spectroscopy, supported by the single-crystal X-ray diffraction of a3, indicates that the gelator molecules are aggregated through intermolecular hydrogen bonding in all of the solvents examined. The thermal stability of the gels in apolar and polar solvents was found to be dependent primarily on the relative strength of intermolecular hydrogen bonding and van der Waals interactions, respectively, compared with the strength of solvent-gelator interactions. The results of DSC indicated that the contribution of the difference in intergelator van der Waals interactions, compared with the gelator-solvent van der Waals and hydrogen bonding interactions, provided by the alkyl tail to the stability of the gel has a linear relationship with the number of methylene units in alkyl chains of length greater than six. In polar solvents, this contribution lies between 3.5 and 4.2 kJ mol(-1) per methylene unit, and in apolar solvents, it is 2.2 kJ mol(-1). The hydrogen bonding interactions were weaker in polar solvents and hence gelation occurred only where sufficient compensation was provided by intergelator van der Waals interactions. The results show that the direct relation of gelation strength to changes in solvent properties is not possible and more complex relationships should be considered. Furthermore, it is apparent that the development of design rules for the construction of LMWG molecules incorporating more than one anisotropic growth element must take into consideration the role of the solvent in determining which of the contributions is dominant.

The dramatically lower volatility of gamma-butyrolactone compared to its open chain analog methyl propionate is analyzed at the molecular dimer level using FTIR spectroscopy in supersonic jets. It is found that the spectral shifts from the monomer to the dimer are about three times more pronounced in the lactone at low temperatures. The spectra are consistent with sandwich-like dimers optimizing their strong dipole-dipole interaction, possibly augmented by specific C-H...O=C hydrogen bond contacts. The spectra show significant evolution from the dimer to the condensed phase, indicative of secondary interactions with the ester oxygen and long range forces. The reduced dipole moment in the open chain ester leads to less specific interactions, unless a trans conformation of the ester group as in the lactones is enforced. The latter is not energetically accessible in open chain esters because it would bring the molecular C=O and C-O-C dipole moments into an unfavorable near-parallel orientation, thus their higher volatility.

The Taft's substituent constant of the pentafluorophenyl group (sigma(C(6)F(5))) was reestimated to be 1.50 by correlation between IR spectral data (v(C)(=)(O)) and sigma constants for a series of esters (involving the pentafluorobenzyl group) of 3-phenylpropanoic acid and butanoic acid. The possibility of the disturbance of the correlation by the intramolecular pi-pi interaction between C(6)F(5) and C(6)H(5) groups in pentafluorobenzyl 3-phenylpropanoate was excluded by ab initio and DFT calculations of the stable conformations and their carbonyl frequencies. The reestimated sigma(C(6)F(5)) value was used for calculation of the pK(a) value of pentafluorobenzyl alcohol [14.5 (or 14.3)].

The work presented here is aimed at determining the potential and limitations of Raman spectroscopy for fat analysis by carrying out a systematic investigation of C4−C24 FAME. These provide a simple, well-characterized set of compounds in which the effect of making incremental changes can be studied over a wide range of chain lengths and degrees of unsaturation. The effect of temperature on the spectra was investigated over much larger ranges than would normally be encountered in real analytical measurements. It was found that for liquid FAME the best internal standard band was the carbonyl stretching vibration ρ(C=O), whose position is affected by changes in sample chain length and physical state; in the samples studied here, it was found to lie between 1729 and 1748 cm−1. Further, molar unsaturation could be correlated with the ratio of the ρ(C=O) to either ρ(C=C) or δ(H−C=) with R
2>0.995. Chain length was correlated with the δ(CH2)tw/ρ(C=O) ratio, (where “tw” indicates twisting) but separate plots for odd- and even-numbered carbon chains were necessary to obtain R
2>0.99 for liquid samples. Combining the odd- and even-numbered carbon chain data in a single plot reduced the correlation to R
2=0.94–0.96, depending on the band ratios used. For molal unsaturation the band ratio that correlated linearly with unsaturation (R
2>0.99) was ρ(C=C)/δ(CH2)sc (where “sc” indicates scissoring). Other band ratios show much more complex behavior with changes in chemical and physical structure. This complex behavior results from the fact that the bands do not arise from simple vibrations of small, discrete regions of the molecules but are due to complex motions of large sections of the FAME so that making incremental changes in structure does not necessarily lead to simple incremental changes in spectra.

The accuracies of the calculated vibrational frequencies and Raman intensities given by two new, highly compact Pol-type basis sets, Z2PolX and Z3PolX, have been determined and compared to the 6-31G(d), PolX, and aug-cc-pVTZ basis sets. Calculation of accurate Raman intensities has previously required large basis sets, but the ZmPolX basis sets are smaller even than PolX, which are the most compact basis sets able to calculate accurate Raman intensities. For the largest compound studied, C5H10O2, Z3PolX required more than an order of magnitude less CPU time than PolX, which has been shown to be 10 times faster than aug-cc-pVTZ. Two sets of test molecules were studied: one was a series of small molecules for which experimental values for absolute Raman activities were available; the second was a series of medium-sized molecules (mainly common organic solvents) where only relative Raman band intensities were available. The accuracies of the Raman intensities given by both of the ZmPolX basis sets were good compared to those of the PolX and aug-cc-pVTZ sets, and much better than the 6-31G(d) values. The errors in even unscaled frequency values <2000 cm(-1) were also acceptable and were slightly lower for Z3PolX than Z2PolX (30 cm(-1) vs. 48 cm(-1)). The combination of good intensity and frequency data meant that for the medium-sized organic molecules there was a close correspondence between the simulated Raman spectra and experimental data, and that the observed bands could easily be assigned on the basis of these calculations. Achieving this level of accuracy in the simulations at modest computational cost should now allow computational methods to be combined with experimental Raman studies much more widely than is currently the case.

Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).

Raman spectroscopy has been used to predict the abundance of the FA in clarified butterfat that was obtained from dairy cows fed a range of levels of rapeseed oil in their diet. Partial least squares regression of the Raman spectra against FA compositions obtained by GC showed that good prediction of the five major (abundance >5%) FA gave R
2=0.74–0.92 with a SE of prediction (RMSEP) that was 5–7% of the mean. In general, the prediction accuracy fell with decreasing abundance in the sample, but the RMSEP was <10% for all but one of the 10 FA present at levels >1.25%. The Raman method has the best prediction ability for unsaturated FA (R
2=0.85–0.92), and in particular trans unsaturated FA (best-predicted FA was 18∶1tΔ9). This enhancement was attributed to the isolation of the unsaturated modes from the saturated modes and the significantly higher spectral response of unsaturated bonds compared with saturated bonds. Raman spectra of the melted butter samples could also be used to predict bulk parameters calculated from standard analyzes, such as iodine value (R
2=0.80) and solid fat content at low temperature (R
2=0.87). For solid fat contents determined at higher temperatures, the prediction ability was significantly reduced (R
2=0.42), and this decrease in performance was attributed to the smaller range of values in solid fat content at the higher temperatures. Finally, although the prediction errors for the abundances of each of the FA in a given sample are much larger with Raman than with full GC analysis, the accuracy is acceptably high for quality control applications. This, combined with the fact that Raman spectra can be obtained with no sample preparation and with 60-s data collection times, means that high-throughput, on-line Raman analysis of butter samples should be possible.

Raman spectroscopy has been used for the first time to predict the FA composition of unextracted adipose tissue of pork, beef, lamb, and chicken. It was found that the bulk unsaturation parameters could be predicted successfully [R
2=0.97, root mean square error of prediction (RMSEP)=4.6% of 4 δ], with cis unsaturation, which accounted for the majority of the unsaturation, giving similar correlations. The combined abundance of all measured PUFA (≥2 double bonds per chain) was also well predicted with R
2=0.97 and RMSEP=4.0% of 4 δ. Trans unsaturation was not as well modeled (R
2=0.52, RMSEP=18% of 4 δ); this reduced prediction ability can be attributed to the low levels of trans FA found in adipose tissue (0.035 times the cis unsaturation level). For the individual FA, the average partial least squares (PLS) regression coefficient of the 18 most abundant FA (relative abundances ranging from 0.1 to 38.6% of the total FA content) was R
2=0.73; the average RMSEP=11.9% of 4 δ. Regression coefficients and prediction errors for the five most abundant FA were all better than the average value (in some cases as low as RMSEP=4.7% of 4 δ). Cross-correlation between the abundances of the minor FA and more abundant acids could be determined by principal component analysis methods, and the resulting groups of correlated compounds were also well predicted using PLS. The accuracy of the prediction of individual FA was at least as good as other spectroscopic methods, and the extremely straightforward sampling method meant that very rapid analysis of samples at ambient temperature was easily achieved. This work shows that Raman profiling of hundreds of samples per day is easily achievable with an automated sampling system.

In this study multivariate analysis of Raman spectra has been used to classify adipose tissue from four different species (chicken, beef, lamb and pork). The adipose samples were dissected from the carcass and their spectra recorded without further preparation. 102 samples were used to create and compare a range of statistical models, which were then tested on 153 independent samples. Of the classical multivariate methods employed, Partial Least Squares Discriminant Analysis (PLSDA) performed best with 99.6% correct classification of species in the test set compared with 96.7% for Principal Component Linear Discrimination Analysis (PCLDA). Kohenen and Feed-forward artificial neural networks compared well with the PLSDA, giving 98.4 and 99.2% correct classification, respectively.

New scaling factors have been determined for obtaining fundamental vibrational frequencies and zero‐point vibrational energies from harmonic frequencies calculated at the HF/6–31G* and MP2/6–31G* levels. The scaling factors for the fundamental frequencies have been derived from a comparison of a total of 1066 calculated frequencies for 122 molecules with corresponding experimental values, while the zero‐point energy scaling factors were determined from a comparison of the computed values with the experimental zero‐point energies for a set of 24 molecules. The scaling factors recommended are, respectively, 0.8929 and 0.9427 for HF/6–31G* and MP2/6–31G* fundamental frequencies, and 0.9135 and 0.9646 for HF/6–31G* and MP2/6–31G* zero‐point energies. RMS errors were determined to be around 50 cm−1 for the HF and MP2 fundamental frequencies, and around 0.4 kJ mol−1 for the HF and MP2 zero‐point energies.

In some esters of formic acid which carry bulky alkyl groups (e .g, t-butyl formate, 1,1-diethylpropyl formate, and triphenylmethyl formate), the presence of s-cis conformer has been confirmed by various spectroscopic techniques. The dipole-moment measurements also support the conclusion drawn from the spectroscopic data.

The molecular structure of silyl acetate has been determined in the gas phase by electron diffraction and in the crystalline state by X-ray diffraction. The Si–O bond length is 1.685(3)Å in the gas and 1.696(4)Å in the solid. In both phases the heavy-atom skeleton is almost planar with the Si–O and CO bonds arranged cis to one another giving intramolecular Si O (carbonyl) distances of 2.795(14)Å(gas) and 2.832(4)Å(solid). The crystal structure is distinguished by having unusually short Si O (carbonyl) intermolecular contacts of length 2.721 (4)Å; these interactions exhibit the stereospecificity associated with secondary bonds. Solid methyl acetate, studied to provide a reference structure, has no short intermolecular contacts.

Geometries and harmonic frequencies of CH4, NH3, H2O, HF, C2H2, C2H4, C2H6, HCN, CO, H2CO and CH3F are calculated via density functional theory (DFT) using the “hybrid” density functionals “Becke3-Lee-Yang-Parr” and “Becke3-Perdew86” at the 6-31G∗ and TZ2P basis set levels. At both basis set levels, the results are in better agreement with experiment than those obtained via DFT using the LSDA and BLYP functionals and via the SCF and MP2 methodologies. At the TZ2P basis set level, the mean absolute deviation of predicted and experimental bond lengths is 0.005 Å for both hybrid functionals; at 6-31G∗ it is 0.006 Å. The mean absolute percentage deviation of predicted and experimental harmonic vibrational frequencies is 1.2% at TZ2P and 1.9–2.0% at 6-31G∗.

Rotations around the neighboring C–C(O) and C(O)–O bonds in two esters, H3C–CH2–C(O)–O–CH3 (I) and H3C–CH(CH3)–C(O)–O–CH3 (II) that represent model molecules for aliphatic main chain and side group polyesters were studied by ab initio and density functional methods (MP2, B3-LYP and B-LYP) using the standard Gaussian basis set 6-31G(d). The performance of the PCFF force field, developed for polymers, to reproduce the conformational behaviors of the C–C and C–O rotations in question was evaluated. Disagreements between the quantum chemical and force field results were removed by reoptimizing the PCFF force field torsion parameters of current interest. The conformational dependence of geometrical parameters and electrostatic potential derived (CHELPG) atomic charges was also studied.

The stable s-trans and s-cis conformations of (E)-3-methyl-3-penten-2-one have been studied using both the Hartree–Fock (HF) and Becke's three-parameter (B3LYP) density functional theory (DFT) with a large Gaussian 6-31G* basis set. We have compared equilibrium geometries, thermal properties of the two conformations, and discussed the potential energy curve of the internal rotation of the molecule. The vibrational frequencies, intensities, and potential energy distributions of the two conformations have been calculated and then compared with experimental IR and Raman spectra. The calculated results show that: (i) there are limited differences for bond angles between the skeleton of the s-trans and that of the s-cis conformation; (ii) the total energy of the s-trans conformation is lower by 0.99kcal/mole than that of the s-cis one, the energy barrier from the s-trans to the s-cis conformation is 9.07kcal/mole, and the two conformations can simultaneously exist; and (iii) the calculated spectra are in good agreement with experimental data.

The quadratic configuration interaction calculation in the Gaussian‐2 second‐order Møller–Plesset perturbation theory approach, G2(MP2), is replaced by a coupled‐cluster (CC) singles and doubles calculation including a perturbational estimate of the triples excitations. In addition, the self‐consistent‐field (SCF) and MP2 geometry optimizations and SCF frequency calculation in the G2(MP2) approach are replaced by a density functional theory geometry optimization and frequency calculation [using the Becke three parameter hybrid functional with the Lee–Yang–Parr non‐local correlation functional (B3LYP)] in the proposed G2(B3LYP/MP2/CC) approach. This simplification does not affect the average absolute deviation from experiment, but decreases the maximum error compared with the G2(MP2) approach. The G2(B3LYP/MP2/CC) atomization energies are compared with those obtained using the B3LYP approach, and the G2(B3LYP/MP2/CC) model is found to be more reliable, even if the B3LYP calculations are performed using a large basis set.

Raman intensities have been computed for a series of test molecules (N2, H2S, H2O, H2CO, CH4, C2H2, C2H4, C2H6, SiO2, NH3, CH2F2, and CH2Cl2) using Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), and density functional theory, including local, gradient-corrected, and hybrid methods (S-VWN, B-LYP and B3-LYP, and MPW1-PW91) to evaluate their relative performance. Comparisons were made with three different basis sets: 6-31G(d), Sadlej, and aug-cc-pVTZ. The quality of basis set used was found to be the most important factor in achieving quantitative results. The medium sized Sadlej basis provided excellent quantitative Raman intensities, comparable to those obtained with the much larger aug-cc-pVTZ basis set. Harmonic vibrational frequencies computed with the Sadlej basis set were in good agreement with experimental fundamentals. For the quantitative prediction of vibrational Raman spectra, the Sadlej basis set is an excellent compromise between computational cost and quality of results. © 1999 American Institute of Physics.

Equations are presented for the analytic determination of dipole moment derivatives with respect to nuclear coordinates for closed‐shell, open‐shell unrestricted, and open‐shell restricted Hartree–Fock wave functions. The efficient evaluation of these derivatives and the resulting infrared intensities simultaneously with determination of the vibrational frequencies is discussed. Intensities are presented for a selection of test molecules with a wide variety of basis sets. It is concluded that basis sets of double‐zeta polarized or higher quality usually give correct qualitative information about the ordering of the intensities, while smaller basis sets may not even predict the most intense mode correctly. Quantitative accuracy using the larger basis sets seems to be limited primarily by the use of the double harmonic approximation.

Two strong carbonyl stretching modes (∼1740 and ∼1720 cm -1) are observed in the Raman spectra of anhydrous crystalline dipalmitoylphosphatidylcholine (DPPC), anhydrous dipalmitoylphosphatidylethanolamine (DPPE), and dilaurylphosphatidylethanolamine (DLPE) cocrystallized with glacial acetic acid (HAc). Evidence is presented which convinces us that the two bands are due to conformation differences in the acyl linkages of the two hydrocarbon chains. Evidence is presented which shows that (1) the C=O stretching frequency is sensitive to rotation about the C 2-C 1 carbon-carbon bond, and is not sensitive to rotation about the C 1-O bond; (2) the higher frequency C=O stretching band arises from an approximately gauche conformation (attributed to the β-chain acyl linkage in the crystalline samples); (3) the lower frequency C=O stretching band arises from an approximately trans conformation (attributed to the γ-chain acyl linkage in the crystalline samples). The relative intensities of these two bands are shown to depend upon the state of the phospholipid sample. The Raman spectra of gel-phase aqueous dispersions of phospholipid samples and partially hydrated DPPC have only one strong Raman C=O band, located at the frequency of the gauche conformer band. The use of the relative intensities of these two bands to determine acyl linkage conformation in the β and γ chains and to estimate the packing arrangement of the two chains is discussed. Raman C=O stretch bandwidths were measured for various phospholipid samples and found to vary greatly as a function of the state (hydration and temperature) of the sample. The use of Raman C=O bandwidths to monitor freedom of motion in the acyl region of phospholipids is also discussed.

Harmonic force fields were calculated using fourth-order Møller-Plesset (MP4) theory for CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, acetylene, HCN, ethylene, formaldehyde, chloromethane, and fluoromethane. These were compared with the experimental force fields. Most of the diagonal force constants for these molecules are computed reliably (1-2% error) at the MP4/6-311+g(2d,2p) level. Exceptions are force constants for out-of-plane bending in the π-bonded molecules and for stretching of the multiple bonds. For computations using second-order Møller-Plesset (MP2) theory, the 6-31g* basis is inferior to basis sets having polarization functions on all atoms such as 6-311+g** and 6-311+g(2d,2p). The force fields computed with MP2 theory are as accurate as those computed at the MP4 level except that HX stretching force constants are consistently overestimated by ca. 3% with MP2 theory. Reduced isotopic partition function ratios, (s2/s1)f, and fractionation factors (FFs) for hydrogen/deuterium substitution were computed for the same set of molecules. The (s2/s1)f values were compared with values computed from experimental harmonic frequencies. The (s2/s1)f values are overestimated by RHF and MP2 theory, but the error is removed when frequencies for the isotopomers are scaled uniformly. The resulting values agree with experiment to within ±2.5% at the MP2 level and ±3.3% at the RHF level.

Predicted vibrational frequencies are reported for 15 small cationic species from Hartree-Fock calculations using the 4-21G and 6-31G* basis sets. Force constants from these calculations were corrected using empirical scale factors taken from a collection of similar neutral molecules. These scale factors reproduce 184 experimental frequencies for the neutral molecules with percent errors of 3.1% and 2.5% for the 4-21G and 6-31G* basis sets, respectively. When these scale factors are applied to the cations, 22 known experimental frequencies are predicted with percent errors of 4.5% and 2.0%, respectively.

Density functional theory (DFT) using the 6-31G* basis set and two nonlocal exchange-correlation functionals (Becke-Lee-Yane-Parr [B-LYP] and the three-parameter compound function of Becke [B3-LYP]) has been used for the calculation of vibrational force fields of a set of 31 organic molecules including a wide range of functional groups. The calculated force constants have been scaled to experimental vibrational frequencies by using (a) an overall scaling constant and (b) a set of 11 factors paying respect to the different kinds of internal coordinates. The comparison of the scaled fundamental frequencies with experiment shows that density functional theory is a reliable tool for the interpretation of IR spectra. The uncorrected DFT frequencies and force constants approximate the experimental ones in a much more uniform fashion than does Hartree-Fock theory. Nevertheless, the use of multiple scale factors leads to further significant improvement. The scaled B3-LYP results are superior to the B-LYP ones, even though the unsealed B-LYP frequencies are, through error cancellation, slightly better than the B3-LYP ones. The reliability of scaled force fields is demonstrated by comparing the calculated and experimental vibrational spectra of aniline.

The performance of semiempirical, ab initio, and density functional methods in calculating and describing the vibrational frequencies of benzene was determined. Different levels were used. The modes were characterized by the magnitude and direction of the displacement vector. The error in the calculated frequencies was reduced using two procedures to obtain the scaled frequencies. Scaling equations were determined for each theoretical method. Specific scale factors were calculated to reduce the error in the ring modes of benzene derivatives. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 661–684, 2000

The basis set polarization method is used to generate the first-order polarized basis sets for Sn, Sb, Te, and I. The standard (spd) and extended (spdf) versions of those basis sets are derived for the purpose of calculations of dipole moments and dipole polarizabilities for molecules involving the fourth-row atoms. The verification of the performance of the generated polarized basis sets is achieved mainly by a cross-examination of different atomic and molecular results calculated in this paper. The role of the core-polarization and relativistic effects is investigated. It is shown that the relativistic contribution to dipole moments of the fourth-row hydrides is commensurate with the contribution due to electron correlation and must be explicitly considered in accurate calculations. The detailed basis set data for Sn through I are presented in the Appendix.

Ethyl formate and other substituted ethyl formates exist in stable anti and gauche conformations about the COCC dihedral angle, according to microwave spectroscopic studies. Similar studies of ethyl thiolformates
characterize stable gauche conformations about the corresponding CSCC dihedral angle in every compound studied, but the anti conformation is found only in ethyl fluorothiolformate and chlorothiolformate. Ab initio calculations that include electron
correlation via MP2 or the B3LYP density functional model have been carried out for ethyl and methyl formate and thiolformate
and their fluoroformate analogs. These calculations reveal that the potential energy minima at gauche and anti COCC configurations are well developed in every case. However, although the gauche minimum for the CSCC torsional angle is clearly defined, the potential function near the anti CSCC configuration corresponds to a potential energy plateau rather than a minimum. In the case of ethyl fluorothiolformate,
a modest well is predicted at the anti CSCC configuration, in agreement with experimental results.

The structure of methyl acetate was studied by joint analysis of gas phase electron diffraction, microwave and IR data, using constraints taken from relaxed 4-21G gradient geometry and force field calculations. All data are in accord with a planar heavy-atom skeleton in the syn conformation. The geometry of methyl acetate in the gas phase is essentially equal to that in the crystal. Some rg—re corrections have been evaluated. Subject to the ab initio constraints the following internal coordinates (r0αstructure) have been found: CO = 1.206 Å, H3CO = 1.438 Å, CO = 1.357 Å, CC = 1.496 Å, 〈CH〉 = 1.078 Å, ∠COC = 116.4°, ∠;OCO = 123.0°.

A comparison of several density functional methods for calculating vibrational frequencies is reported. Methods examined include the local S-VWN (LSDA) functional, the non-local B-LYP and B-VWN functionals and the hybrid B3-LYP and B3-P86 functionals. The split-valence polarized 6-31G∗ basis set has been used in all methods. The computed frequencies were compared with experimental frequencies for a set of 122 molecules (a total of 1066 frequencies). All density functional theory (DFT) methods perform well for the calculation of vibrational frequencies, with overall root mean square errors (34–48 cm−1) significantly less than that reported for the MP2 theory (61 cm−1). The two hybrid functionals (B3-LYP and B3-P86) are more reliable than the S-VWN, B-LYP and B-VWN functionals. Scaling factors recommended for reproducing experimental fundamentals are 0.9833, 0.9940, 0.9820, 0.9613 and 0.9561, for S-VWN, B-LYP, B-VWN, B3-LYP and B3-P86, respectively. The performance of the various DFT methods on the calculation of zero-point energies is compared with experimental results for 24 molecules. Again, the hybrid functionals represent a significant improvement over the local and non-local density functionals.

IR spectra of methyl formate and methyl acetate have been studied by trapping thermal molecular beams in Ar matrices. For methyl formate, four bands have been assigned to the anti conformer. ΔHo (anti-syn) for the conformational equilibrium is 4750 ± 190 cal mol−1. In methyl acetate there is an increase in ΔHo due to steric hindrance between the methyl groups.

Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree?Fock (HF), M?ller?Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT:? B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vibrations were obtained from least-squares fits of inverse frequencies. ZPVE scaling factors were obtained from a comparison of the computed ZPVEs (derived from theoretically determined harmonic vibrational frequencies) with ZPVEs determined from experimental harmonic frequencies and anharmonicity corrections for a set of 39 molecules. Finally, scaling factors for theoretical frequencies that are applicable for the computation of thermal contributions to enthalpy and entropy have been derived. A complete set of recommended scale factors is presented. The most successful procedures overall are B3-PW91/6-31G(d), B3-LYP/6-31G(d), and HF/6-31G(d).

This study examined the effects of polymeric components on the physical state of chlorhexidine within bioadhesive, semisolid formulations using Raman spectroscopy. Semisolid formulations were prepared in which chlorhexidine base (CHX, 5%w/w, particle size <63 microm) was dispersed in aqueous (phosphate-buffered saline, pH 6.8) polymer matrices consisting of one or more polymeric components, namely HEC (3%w/w), PVP (3%), and PC (PC, 3%). Raman spectra were recorded using 785-nm excitation and were typically accumulated for 360 s. The Raman spectra were dominated by the presence of CHX. The spectra of CHX in HEC and in HEC/PVP gels were indistinguishable from that for solid CHX as a result of the insolubility of CHX in these formulations. However, in systems containing PC and CHX, there was a shift in the strongest band from 1564 cm(-1) to 1608 cm(-1), which may be accredited to protonation of the basic CHX by the numerous carboxylic acidic groups on PC. Identical shifts in the band positions were observed when this protonation was modeled using ethanoic acid, supporting the view that there was a simple acid base reaction between PC and CHX. However, there were notable differences in the relative intensities of the peaks from these samples, with the spectrum of CHX in the PC matrix displaying properties intermediate between those of CHX dissolved in ethanoic acid and solid CHX diacetate. This may be accredited to the limited solubility of the CHX-PC ion pair. In matrices containing HEC and PC, no peak was observed at 1564 cm(-1), whereas the intensity of the peak at 1608 cm(-1) was increased. Therefore, in these formulations CHX was completely converted to the di-cation as a result of the synergistic effects of PC (which protonated CHX) and HEC (which solubilized the di-cation). In the absence of either HEC or PC, complete protonation was not achieved. It is suggested that this enhancement of solubility of H(2)CHX(2+) may be due to hydrogen bonding, given the hydroxylated nature of HEC. In conclusion, this study has shown the applicability of Raman spectroscopy for both the analysis of opaque, semisolid formulations and, additionally, for the examination of the state of therapeutic agents within such matrices. In particular, using Raman spectroscopy, it was uniquely possible to identify the roles of various polymeric components on both the ionization and solubilization of CHX within aqueous semisolid systems.

Recent spectroscopic advances have led to the first determinations of infrared vibration-rotation bands of polyatomic molecular ions. These initial detections were guided by ab initio predictions of the vibrational frequencies. The calculations reported here predict the vibrational frequencies of additional ions which are candidates for laboratory analysis. Vibrational frequencies of neutral molecules computed at three levels of theory, HF/3-21G, HF/6-31G*, and MP2/6-31G*, were compared with experiment and the effect of scaling was investigated to determine how accurately vibrational frequencies could be predicted. For 92% of the frequencies examined, uniformly scaled HF/6-31G* vibrational frequencies were within 100 cm-1 of experiment with a mean absolute error of 49 cm-1. This relatively simple theory thus seems suitable for predicting vibrational frequencies to guide laboratory spectroscopic searches for ions in the infrared. Hence, the frequencies of 30 molecular ions, many with astrochemical significance,were computed. They are CH2+, CH3+, CH5+, NH2+, NH4+, H3O+, H2F+, SiH2+, PH4+, H3S+, H2Cl+, C2H+, classical C2H3+, nonclassical C2H3+, nonclassical C2H5+, HCNH+, H2CNH2+, H3CNH3+, HCO+, HOC+, H2CO+, H2COH+, H3COH2+, H3CFH+, HN2+, HO2+, C3H+, HOCO+, HCS+, and HSiO+.

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- Fig

Fig. 10. The 14 conformations of C 4 H 8 O 2 that correspond to stable geometries (Table 5). The sets of conformations {a, b, c and d} and {s, t, ee
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