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Efficient scheme for construction of physically justified STO##-3Gel and STO##-3Gmag basis sets has been proposed. It is based upon the analysis of analytical form of the first-order correction functions to unperturbed STO basis sets under the perturbation by electric or magnetic fields. The test calculations of polarizability, magnetic susceptibility and chemical shifts performed for a series of aromatic compounds within the developed basis set in the framework of Hartree-Fock and Density Functional Theory (DFT) approaches show good agreement of the predicted properties with experiments. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

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... To account for the solvent effect, the SMD model with methanol (ε = 32.613) as a solvent was applied. The UV-vis calculations were performed at SMD/ PBE1PBE level using developed in our group STO ## -3G el basis set [37], which demonstrated high efficiency for electric and magnetic properties calculation [35]. The intensities of the calculated spectra were scaled using Gabedit program [38] to fit the most intensive band obtained experimentally. ...

... There is no correlation between the wavelength of the shortest band of UV-vis spectra of compounds 1-6 and the HOMO/LUMO energy gap (Tables 2 and 4), which is in consistence with involving several molecular orbitals in transition. The calculations, performed at SMD/PBE1PBE level using developed in our group STO ## -3G el basis set [37], demonstrate high efficiency for UV-vis spectra simulation and allow to determine the relative stability of different tautomers of 2-(3-hetaryl-1,2,4triazol-5-yl)anilines as well as 2-(3-(methoxyphenyl)-1,2,4triazole-5-yl)anilines that were shown in our previous work [35]. Table 3 contains calculated dipole moments for all compounds in the gas phase and methanolic solution. ...

1,2,4-Triazole is a popular scaffold in drug design. According to chemical nature, the triazole ring tends to prototropic tautomerism. Tautomeric phenomena are important for studying the chemical reactivity and interaction of drugs based on triazole with biomolecules in the human body. Theoretical modeling was used to assign structures of newly synthesized 2-(3-hetaryl-1,2,4-triazol-5-yl)anilines. The procedure included quantum-chemical SMD/M06-2X/6–311++G(d,p) calculation of the relative stability for possible tautomers, simulation of UV/vis spectra for the most stable forms, and comparison of the resulting curves with the experimental spectral data taking into account the Boltzmann weighting. The influence of the substituents in triazole ring on tautomeric equilibrium was elucidated. NBO charge distribution, dipole moment, molecular electrostatic potential, and HOMO/LUMO gap for the most stable tautomers were analyzed.

... We have proposed in [20,21] a scheme for augmentation of basis sets which is based upon the expansion of the first-order correction functions on the unperturbed basis functions obtained applying perturbation theory for atomic orbitals (AO). Such approach for the construction of physically-adapted basis sets have been used by us in [22] where STO ## -3G mag and STO ## -3G el sets have been proposed for the calculation of magnetic or electric properties of molecules. These basis sets have been used in [23][24][25]. ...

... The values of energies for these atoms obtained using new coefficients show the opportunity to improve well-known STO-3G basis set. The STO(0)-3G set of atomic orbitals has been extended using the approach described in papers [22,33] by adding new basis AOs extracted from first-order correction functions to unperturbed Slater AOs in case of magnetic uniform field. ...

The new approach for the determination of orbital exponents and contracted coefficients for STO-3G family basis sets has been proposed. Calculations of the necessary coefficients have been performed using Mathcad program package with Minerr solving block. This approach has been used to perform the approximation of the Slater-type orbital (STO) by three Gaussian-type orbitals (GTO). The performance of such modified basis sets has been tested for the calculations of atomic energies using STO(0)-3G basis set and for nuclear magnetic shielding tensors using STO(1M)-3G basis set. The obtained atomic energies are characterized by lower values than those calculated using old parameters. The results for ¹H and ¹³C chemical shifts calculations demonstrate better agreement with the experimental data compared to the data obtained using standard basis sets, such as 6-311G (2d, p), cc-pVDZ and pcS-1. Required time of calculations using the basic set suggested by us is less than the time spent on the calculation using standard basic sets with a similar number of basis functions. Physically adapted and at the same time small by size basic set STO(1M)-3G is perspective for the calculation of magnetic properties of big molecular systems. Proton and ¹³C chemical shifts have been calculated for molecules of adenosine monophosphate (AMP) and flavinadenine dinucleotide (FAD), that play an important role in various biological processes. For both molecules the results of the calculation have shown values close to the experimental data.

... where AB = H 2 , N 2 , O 2 , CO, NO and E(SWCNT· · ·AB), E(SWCNT) and E(AB) are the corresponding energies of the optimized adduct, nanotube and the covalently adsorbed molecule, respectively. The GIAO NMR [17,[27][28][29][30][31][32] calculations on previously optimized structures were performed using the CAM-B3LYP/STO-3G mag level of theory [43,44]. The CAM-B3LYP [43] density functional was recently used for accurate prediction of 13 C NMR shieldings in fullerenes [45] and van der Waals dimers [46]. ...

... The CAM-B3LYP [43] density functional was recently used for accurate prediction of 13 C NMR shieldings in fullerenes [45] and van der Waals dimers [46]. The modified STO-3G basis set was recently introduced [44] as an efficient alternative for accurate calculations of carbon nuclear magnetic shieldings. Its excellent performance was recently confirmed [47][48][49]. ...

... where AB = H 2 , N 2 , O 2 , CO, NO and E(SWCNT· · ·AB), E(SWCNT) and E(AB) are the corresponding energies of the optimized adduct, nanotube and the covalently adsorbed molecule, respectively. The GIAO NMR [17,[27][28][29][30][31][32] calculations on previously optimized structures were performed using the CAM-B3LYP/STO-3G mag level of theory [43,44]. The CAM-B3LYP [43] density functional was recently used for accurate prediction of 13 C NMR shieldings in fullerenes [45] and van der Waals dimers [46]. ...

... The CAM-B3LYP [43] density functional was recently used for accurate prediction of 13 C NMR shieldings in fullerenes [45] and van der Waals dimers [46]. The modified STO-3G basis set was recently introduced [44] as an efficient alternative for accurate calculations of carbon nuclear magnetic shieldings. Its excellent performance was recently confirmed [47][48][49]. ...

... This basis set was downloaded from Environmental Molecular Sciences Laboratory (EMSL) exchange basis set library [71,72]. Finally, we selected somehow smaller and more compact STO-3G mag basis set, designed by Leszczyński and coworkers [73] for efficient prediction of carbon shieldings in larger molecular systems. The latter basis sets was taken directly from their article [73]. ...

... Finally, we selected somehow smaller and more compact STO-3G mag basis set, designed by Leszczyński and coworkers [73] for efficient prediction of carbon shieldings in larger molecular systems. The latter basis sets was taken directly from their article [73]. ...

The applicability of popular and efficient B3LYP hybrid density functional and medium-size Pople-type basis set in combination with computationally expensive anharmonic model to obtain more accurate theoretical structure, vibrational frequencies and GIAO NMR parameters of cytosine was tested. We report on prediction of cytosine equilibrium (R
e
) and rovibrationally averaged (R
v
) structures and vibrational frequencies in the gas phase and DMSO solution using density functional theory combined with 6-311++G** basis set. The harmonic and anharmonic vibrational frequencies (using second-order vibrational perturbation theory, VPT2) were critically discussed. In comparison with initial harmonic data, a significantly better agreement between scaled and anharmonic frequencies and experiment was observed. Proton and carbon nuclear magnetic shieldings were calculated at R
e
and R
v
structures of cytosine in the gas phase and DMSO solution using BHandH and B3LYP density functionals combined with 6-311++G**, aug-cc-pVTZ-J and STO-3Gmag basis sets. The obtained NMR results were compared with available experimental data and discussed at length.

... The gauge including atomic orbital [51,52] (GIAO) calculations of nuclear isotropic shieldings for optimized UB3LYP/6-31G* geometries were performed using the BHandH [43,44] functional and the STO-3G mag basis set [53]. The BHandH [44] density functional and a modified basis set were successful in calculating carbon nuclear shieldings (and chemical shifts) in earlier studies on hydrocarbons, small molecules or nanocarbons [15,36,50,[54][55][56][57]. ...

... The STO-3G mag basis set was developed for accurate description of magnetic properties with a reasonable effort. Leszczyński and coworkers' idea of STO-3G mag basis set arises from an extension of standard STO-3G basis set by functions obtained from analytical first-order corrections using the Green's function [53]. This modified STO-3G basis set shows a very good accuracy, comparable to Jensen's pcS-2 basis set [58], dedicated to accurate prediction of nuclear shieldings, while being half the size of the latter [50]. ...

... The aug-cc-pVTZ-J basis set was downloaded from EMSL. 43 Recently, Leszczynski and coworkers 44 proposed modified basis sets STO-3G mag for efficient calculations of NMR shieldings. So, in this work, we want to test the performance of their basis sets 44 in nuclear shieldings calculation for model peptides. ...

Effective peptidomimetics should posses structural rigidity and appropriate interaction pattern leading to potential spatial and electronic matching to the target receptor site. Rational design of such small bioactive molecules could push chemical synthesis and molecular modeling toward faster progress in medicinal chemistry. Conformational properties of N-t-butoxycarbonyl-glycine-(E/Z)-dehydrophenylalanine N',N'-dimethylamides (Boc-Gly-(E/Z)-ΔPhe-NMe2 ) in chloroform were studied by NMR and IR spectroscopy. The experimental findings were supported by extensive calculations at DFT(B3LYP, M06-2X) and MP2 levels of theory and the β-turn tendency for both isomers of the studied dipeptide were determined in vacuum and in solution. The theoretical data and experimental IR results were used as an additional information for the NMR-based determination of the detailed solution conformations of the peptides. The obtained results reveals that N-methylation of C-terminal amide group changes dramatically the conformational properties of studied dehydropeptides. Theoretical conformational analysis reveals that the tendency to adopt β-turn conformations is much weaker for the N-methylated Z isomer (Boc-Gly-(Z)-ΔPhe-NMe2 ), both in vacuum and in polar environment. On the contrary, N-methylated E isomer (Boc-Gly-(E)-ΔPhe-NMe2 ) can easier adopt β-turn conformation, but the backbone torsion angles (ϕ1 , ψ1 , ϕ2 , ψ2 ) are off the limits for common β-turn types.

... The latter functional was recently introduced for 1 H and 13 C chemical shift calculations. For the calculation of nuclear shieldings, we used 6−311 + G(2d,p), aug-cc-pVQZ basis sets and a relatively small and efficient STO(1M)−3G one, designed by Leszczynski et al. [73,74], for the accurate prediction of 13 C NMR chemical shifts in large hydrocarbons. ...

We report on the density functional theory (DFT) modelling of structural, energetic and NMR parameters of uracil and its derivatives (5-halogenouracil (5XU), X = F, Cl, Br and I) in vacuum and in water using the polarizable continuum model (PCM) and the solvent model density (SMD) approach. On the basis of the obtained results, we conclude that the intramolecular electrostatic interactions are the main factors governing the stability of the six tautomeric forms of uracil and 5XU. Two indices of aromaticity, the harmonic oscillator model of aromaticity (HOMA), satisfying the geometric criterion, and the nuclear independent chemical shift (NICS), were applied to evaluate the aromaticity of uracil and its derivatives in the gas phase and water. The values of these parameters showed that the most stable tautomer is the least aromatic. A good performance of newly designed xOPBE density functional in combination with both large aug-cc-pVQZ and small STO(1M)−3G basis sets for predicting chemical shifts of uracil and 5-fluorouracil in vacuum and water was observed. As a practical alternative for calculating the chemical shifts of challenging heterocyclic compounds, we also propose B3LYP calculations with small STO(1M)−3G basis set. The indirect spin–spin coupling constants predicted by B3LYP/aug-cc-pVQZ(mixed) method reproduce the experimental data for uracil and 5-fluorouracil well.

... Chemical shifts were obtained using benzene and TMS as a reference. In addition, for efficient calculation of nuclear shieldings, we also used a newly modified STO-3G mag basis set [46]. Thus, we decided to test a performance of this basis set in case of NMR parameters of model peptides. ...

Conformational propensities of N-t-butoxycarbonyl-glycine-(E/Z)-dehydrophenylalanine N′-methylamides (Boc-Gly-(E/Z)-ΔPhe-NHMe) in chloroform were investigated by NMR and IR techniques. The low-temperature crystal structure of the E isomer was determined by single crystal X-ray diffraction and the experimental data were elaborated by theoretical calculations using DFT (B3LYP, M06-2X) and MP2 approaches. The β-turn tendencies for both isomers were determined in the gas phase and in the presence of solvent. The obtained results reveal that the configuration of ΔPhe residue significantly affects the conformations of the studied dehydropeptides. The tendency to adopt β-turn conformations is significantly lower for the E isomer (Boc-Gly-(E)-ΔPhe-NHMe), both in gas phase and in chloroform solution.

... Density functionals (B3LYP [28], PBE0 [29], BHandHLYP [30] and VSXC [31]) were used recently for predicting geometrical structure and energy parameters of nanotubes and fullerenes [32÷35]. NMR parameters for carbon nanotubes (geometrical structures were optimized at level B3LYP/6-31G*) were calculated using density functional VSXC and specifically modified basis set STO-3G mag [36]. Both functional VXSC and modified "Leszczynski's" basis set (not to be confused with original and very inaccurate set STO-3G) were used successfully for prediction of chemical shifts 13 C NMR in a number of medium-and macromolecular compounds [32]. ...

... У роботі [54] було продемонстровано, що спектри поглинання азосполук отриманих на основі α-та β-похідних фенілнафтиламінів, суттєво відрізняються. За допомогою функціоналу PBE1PBE з використанням базисних функцій STO##-3Gel [55], який показав високу ефективність для розрахунків електронних спектрів [56], розраховані спектри поглинання для трьох форм сполуки 4а. Вплив розчинника (діоксану), в якому було записано експериментальний спектр, враховувався за сольватаційною моделлю SMD. ...

Досліджено реакцію азосполучення ряду ізомерних N-толіл-1-нафтиламінів та N-толіл-2-нафтиламінів. Представлені результати теоретичного дослідження таутомерних, конформаційних властивостей і величин хімічних зсувів ядер в спектрах 1Н ЯМР для 1- (4-нітрофенілазо) -N-фенілнафтил-2-аміну; 1- (4-нітрофенілазо) -N-п-толілнафтил-2-аміну та 4-(4-нітрофенілазо)-N-фенілнафтил-1-аміну. Розрахунки проведені методом теорії функціонала густини B3LYP з використанням фізично адаптованого для розрахунку магнітних властивостей набору базисних функцій 6-31G_JSKE методами CSGT і GIAO. Вплив розчинника (CDCl3), враховувалося методом SMD. Стабільність можливих конформерів і таутомерних форм встановлена на основі розрахованих в наближенні M06-2X / 6-311 ++ G ** величин вільної енергії Гіббса. Заселеність кожної конформації була розрахована за методом Больцмана. Наведено дані теоретичних розрахунків спектрів поглинання азокбарвника 1-(4-нітрофенілазо)-N-фенілнафтил-2-аміну (4а) методом PBE1PBE / STO ## - 3Gel. Дані теоретичного дослідження спектральних характеристик досліджуваних азобарвників добре корелюють з отриманими експериментальними даними і підтверджують переважне існування азосполук ряду N-арил-2-нафтиламіну у вигляді азо-таутомерів з внутрішньомолекулярним водневим зв'язком.

Structures of selected 3,6-dihalogeno-N-alkyl carbazole derivatives were calculated at the B3LYP/6-311++G(3df,2pd) level of theory, and their (13) C nuclear magnetic resonance (NMR) isotropic shieldings were predicted using density functional theory (DFT). The model compounds contained 9H, N-methyl and N-ethyl derivatives. The relativistic effect of Br and I atoms on nuclear shieldings was modeled using the spin-orbit zeroth-order regular approximation (ZORA) method. Significant heavy atom shielding effects for the carbon atom directly bonded with Br and I were observed (~-10 and ~-30 ppm while the other carbon shifts were practically unaffected). The decreasing electronegativity of the halogen substituent (F, Cl, Br, and I) was reflected in both nonrelativistic and relativistic NMR results as decreased values of chemical shifts of carbon atoms attached to halogen (C3 and C6) leading to a strong sensitivity to halogen atom type at 3 and 6 positions of the carbazole ring. The predicted NMR data correctly reproduce the available experimental data for unsubstituted N-alkylcarbazoles. Copyright © 2013 John Wiley & Sons, Ltd.

An efficient procedure for construction of physically rationalized Slater-type basis sets for calculations of dynamic hyperpolarizability is proposed. Their performance is evaluated for the DFT level calculations for model molecules, carried out with a series of functionals. Advantages of new basis sets over standard d-aug-cc-pVTZ and recently developed LPOL-(FL,FS) Gaussian-type basis sets are discussed. © 2014 Wiley Periodicals, Inc.

The interaction of phenylalanine diamide (Ac-Phe-NHMe) with egg yolk lecithin (EYL) in chloroform was studied by (1) H and (13) C NMR. Six complexes EYL-Ac-Phe-NHMe, stabilized by N-H···O or/and C-H···O hydrogen bonds, were optimized at M06-2X/6-31G(d,p) level. The assignment of EYL and Ac-Phe-NHMe NMR signals was supported using GIAO (gauge including atomic orbital) NMR calculations at VSXC and B3LYP level of theory combined with STO-3Gmag basis set. Results of our study indicate that the interaction of peptides with lecithin occurs mainly in the polar 'head' of the lecithin. Additionally, the most probable lecithin site of H-bond interaction with Ac-Phe-NHMe is the negatively charged oxygen in phosphate group that acts as proton acceptor. Copyright © 2014 John Wiley & Sons, Ltd.

New adjusted Gaussian basis sets are proposed for first and second rows elements (H, B, C, N, O, F, Si, P, S, and Cl) with the purpose of calculating linear and mainly nonlinear optical (L–NLO) properties for molecules. These basis sets are new generation of Thakkar-DZ basis sets, which were recontracted and augmented with diffuse and polarization extrabasis functions. Atomic energy and polarizability were used as reference data for fitting the basis sets, which were further applied for prediction of L–NLO properties of diatomic, H2, N2, F2, Cl2, BH, BF, BCl, HF, HCl, CO, CS, SiO, PN, and polyatomic, CH4, SiH4, H2O, H2S, NH3, PH3, OCS, NNO, and HCN molecules. The results are satisfactory for all electric properties tested; dipole moment (µ), polarizability (α), and first hyperpolarizability (β), with an affordable computational cost. Three new basis sets are presented and called as NLO-I (ADZP), NLO-II (DZP), and NLO-III (VDZP). The NLO-III is the best choice to predict L–NLO properties of large molecular systems, because it presents a balance between computational cost and accuracy. The average errors for β at B3LYP/NLO-III level were of 8% for diatomic molecules and 14% for polyatomic molecules that are within the experimental uncertainty. © 2014 Wiley Periodicals, Inc.

Rapid growth of nanoscience and nanotechnology requires new and more powerful modeling tools. Efficient theoretical modeling of large molecular systems at the ab initio and Density Functional Theory (DFT) levels of theory depends critically on the size and completeness of the basis set used. The recently designed variants of STO-3G basis set (STO-3Gel, STO-3Gmag), modified to correctly predict electronic and magnetic properties were tested on simple models of pristine and functionalized carbon nanotube (CNT) systems and fullerenes using the B3LYP and VSXC density functionals. Predicted geometries, vibrational properties, and HOMO/LUMO gaps of the model systems, calculated with typical 6-31G* and modified STO-3G basis sets, were comparable. The 13C nuclear isotropic shieldings, calculated with STO-3Gmag and Jensen’s polarization consistent pcS-2 basis sets, were also identical. The STO-3Gmag basis sets, being half the size of the latter one, are promising alternative for studying 13C nuclear magnetic shieldings in larger size CNTs and fullerenes.

The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all‐electron electronic structure calculations in general—the linear combination of atomic orbitals (LCAO) method—is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform all‐electron Hartree‐Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.

Nuclear shieldings and chemical shifts of 5‐fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model (PCM) using B3LYP density functional and revised STO(1M)‐3G basis set. For comparison, seven arbitrary selected basis sets including STO‐3G, medium‐size Pople‐ and larger dedicated Jensen‐type ones were applied. The former basis sets were significantly smaller but the calculated structural parameters, harmonic vibrational frequencies were very accurate and close to those, obtained with larger, polarization‐consistent ones. The predicted ¹³C and ¹H chemical shieldings of 5‐fluorocytosine and cytosine, selected as parent molecule, were acceptable (RMS for ¹³C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those, calculated with large basis sets, dedicated for prediction of NMR parameters.

Theoretical investigations of the conformational properties and 1H NMR chemical shifts for N-methyl-4-tolyl-1-(4-bromonaphthyl)amine and N-phenyl-1-(4-bromonaphthyl)amine are reported. The calculations were performed at the DFT level (PBE1PBE functional) using magnetically consistent 6-31G## and STO##-3Gmag basis sets. Conformational properties of the amines were studied using potential energy surface scanning. Chemical shifts were calculated using the GIAO and CSGT methods and averaged in proportion to the population of the corresponding conformations. Solvent effects (CDCl3) were accounted via PCM method. The obtained results allowed to assign the 1H NMR signals for the naphthalene moiety, which could not be done based on the experimental data alone.

An efficient approach for construction of physically justified STO(II)-3Gmag family basis sets for calculation of molecules magnetic properties has been proposed. The procedure of construction based upon the taken into account the second order of perturbation theory in the magnetic field case. Analytical form of correction functions has been obtained using the closed representation of the Green functions by the solution of nonhomogeneous Schrödinger equation for the model problem of "one-electron atom in the external uniform magnetic field". Their performance has been evaluated for the DFT level calculations carried out with a number of functionals. The test calculations of magnetic susceptibility and 1H nuclear magnetic shielding tensors demonstrated a good agreement of the calculated values with the experimental data.

Determining the structure of saccharides in their native environment is crucial to understanding their function and more accurately targeting their utilization. Nuclear magnetic resonance observables such as the nuclear Overhauser effect or spin-spin coupling constants are routinely utilized to study saccharides in their native water environment. However, while highly sensitive to the local environment, chemical shifts are mostly overlooked, despite being commonly measured for compounds identification. Although chemical shifts carry considerable structural information, their direct association with structure is notoriously difficult. This is mostly due to the similarity in the chemical nature of most saccharides causing similar physicochemical environments close to sugar C and H atoms, resulting in comparable chemical shifts. The rise of computational power allows one to compute reliable chemical shifts and use them to determine atomistic details of these sugars in solution. However, any prediction is severely limited by the computational protocol used and its accuracy. In this work, we studied a set of 31 saccharides on which we evaluated various computational protocols to calculate the total number of 375 1H and 327 13C chemical shifts of sugars in an aqueous environment. Our study proposes two cost-effective protocols for simulating 1H and 13C chemical shifts that we recommend for further use. These protocols can help with the interpretation of experimental spectra, but we also show that they are also capable of structure prediction independently. This is possible because of the low mean absolute deviations of calculated shifts from the experiment (0.06 ppm for 1H and 1.09 ppm for 13C). We explore different solvation methods, basis sets, and optimization schemes to reach such accuracy. A correct sampling of the conformation phase space of flexible sugar molecules is also key to obtaining accurately converged theoretical chemical shifts. The linear regression method was applied to convert the calculated isotropic nuclear magnetic shielding constants to simulated chemical shifts comparable with the experiment. The achieved level of accuracy can help in utilizing chemical shifts for elucidating the 3D atomistic structure of saccharides in aqueous solutions. All linear regression parameters obtained on our extensive set of sugars for all the tested protocols can be reutilized in future works.

The reaction of 2-aryl-[1,2,4]triazolo[1,5-c]quinazolines with nucleophilic reagents (hydrazine hydrate, sodium hydroxide, sodium methoxide, hydrochloric acid) under acidic conditions leads to formation of compounds which tend to tautomerism. The products of the transformation are distinguished by the position (ortho-, meta-, para-) of the OCH3 group in the aryl moiety. To assign their structures we used the combined approach: experiment and theoretical modeling. The procedure included calculation of the relative stability for possible tautomers, simulation of UV/Vis spectra for the most stable forms and comparison of the resulting curves with the experimental spectral data taking into account the Boltzmann weighting. Through computations, we showed that the orientation of OCH3 substituent remarkably impacts on the tautomeric behavior of triazoles. In the case of ortho-OCH3 it is controlled by formation of the intramolecular hydrogen bond while for meta- and para- derivatives the degree of conjugation plays the decisive role. In order to balance the accuracy and cost of calculations we evaluated the performance of selected DFT methods and 6-31G*, 6-311++G**, STO##-3Gel basis sets. The last one is physically justified basis set previously constructed in our group and its combination with PBE1PBE approach shown to be the best choice for UV/Vis simulations in the frame of the current research.

PAHs, short for polycyclic aromatic hydrocarbons, are a ubiquitous group of chemically related, environmentally persistent organic compounds having diverse structures and varied toxicity. They have been shown to cause mutagenic and carcinogenic effects on organisms and are quite immunosuppressive. Time-dependent density functional theory (TD-DFT) offers a practical means of understanding the behavior of excitation energies for PAHs. Here, we examined the performance of the long-range corrected Coulomb-attenuating functional (CAM-B3LYP) in relation to four different basis sets, determining which basis set compliments the functional better in identifying the most reactive atomic site on six isomeric PAH compounds. Condensed Fukui function indices were used to compare the performance of applied basis sets in identifying the most reactive atomic site on six isomeric PAHs compounds, assessing which basis set would be more appropriate in determining the site where free-radical formation would occur after light irradiation. Dunning’s correlation consistent triple-zeta (cc-pVTZ) basis set was determined to have the best PAH characterization performance, concluding the need for application of a higher-level basis set with the long-range corrected Coulomb-attenuating functional. Although each compound was a structural isomer of the other, the reactive atomic sites varied for each molecule with the use of an applied basis set. It was concluded that structural shape has some influence on the calculation of PAH characteristics. Lastly, in order to predict DNA single-stranded cleavage factor for the compounds proposed here, we have used the quantitative structure-activity relationship (QSAR). The cleavage factor values for the set of aromatic molecules with similar structures have been collected from the literature for a total number of 22 compounds.

The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general – the linear combination of atomic orbitals (LCAO) method – is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, e.g. finite differences, finite elements, or the discrete variable representation, which are also briefly introduced.
Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform all-electron Hartree–Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.

Exponential dependencies between locally calculated geometric and magnetic indexes of aromaticity, HOMA and NICS(0), NICS(1) and NICS(1)zz and the number of conjugated benzene rings in linear acenes, from benzene to decacene were observed at B3LYP/6‐311+G** level of theory. Correlations between HOMA and NICS indexes showed exponential dependencies and were fitted with simple three‐parameter function. Similar correlations between both indexes of aromaticity and proton and carbon nuclear isotropic shieldings of individual acene rings were observed. Contrary to proton data, the predicted 13C nuclear isotropic shieldings of carbon atoms belonging to inner rings in polyacenes were less shielded indicating lower aromaticity and therefore, higher reactivity.

The results of theoretical and experimental investigation of O-17 NMR chemical shifts for a number of epoxidic compounds are reported. The calculations were performed for the MP2/6-311G(d) level reference geometries using the GIAO and CSGT methods within the coupled Hartree-Fock perturbation theory. Various basis sets were applied in calculations of the chemical shifts. The performance of recently developed magnetically consistent basis sets and their advantages over the standard ones are discussed. The obtained results allow one to assign NMR signals for epoxides for which experimental data were obtained for the mixtures of stereoisomers.

Two methods of physically justified improvement of the STO and GTO basis set quality are suggested for ab initio calculations of molecular magnetic properties. They are based on the analysis of analytical expressions for the first-order correction (response) functions to the unperturbed basis AO's. The response functions have been obtained by solution of the inhomogeneous Schrödinger equation for the model problem “a one-electron atom in an external uniform field”, by the closed representation of the Green's function. It has been shown that unlike the London orbitals for magnetic field the Green's function method enables us to get the general solutions of the inhomogeneous Schrödinger equation. The methods elaborated have been applied in test calculations of magnetic susceptibilities and nuclear shielding constants of the first- and second-row hydrides and diatomics in STO-NG, split-valence CGTO basis sets, and extended ones constructed on their base. Analysis of results obtained has allowed us to determine the field of applicability for the suggested methods of basis set construction adapted for the magnetic properties calculations.

Least‐squares representations of the 3s and 3p Slater‐type atomic orbitals by a small number of Gaussian functions are presented. The use of these Gaussian representations in self‐consistent molecular orbital calculations extends our previous study to molecules containing second row elements. Calculated atomization energies, electric dipole moments, and atomic charges are shown to rapidly converge (with increasing number of Gaussians) to their Slater limits. Results of valence shell optimization studies on a series of second‐row compounds are nearly independent of the level of the Gaussian approximation, and they allow a set of standard molecular ξ exponents to be proposed.

A method is presented that combines quantum mechanical shift calculations with empirical corrections to yield isotropic 13C nuclear magnetic resonance (NMR) shifts for organic molecules in good agreement with experiment. A comparison is made between shifts calculated using Hartree–Fock (HF), Møller–Plesset perturbation theory (MP2), and density functional theory (DFT). The absolute shifts calculated by these methods are translated into shifts relative to tetramethylsilane (TMS) using a simple empirical formula with parameters determined over a set of 37 small organic compounds. It is shown that DFT calculations using small basis sets correlate with experiments well enough that the empirical correction allows experimental shifts to be reproduced to within an RMS error of 4–5 parts per million (ppm). Carbons attached to chlorine, bromine, and iodine are treated with the same empirical corrections but with parameters of different values because of the lack of spin orbit corrections in the calculations; however, these carbons are predicted as accurately as other carbons in the data set. Two models are presented; one is applicable to very large molecules. The empirical corrections developed for these models can be used to predict shifts in a wide variety of organic molecules. One of the models is applied to a moderately sized dye molecule that contains an intramolecular hydrogen bond to demonstrate the utility of using an inexpensive quantum mechanics-based method over an empirical fragment-based method.

The method of McWeeny for estimating magnetic effects due to pi electrons in condensed, benzenoid hydrocarbons is applied to calculate the 97 distinct 'ring currents', and sigma ratios (H'/H'benzene) for the 219 chemically-non-equivalent protons in the 21 planar hexacyclic benzenoid hydrocarbons which have been synthesized. Trends in the 'ring currents' and sigma ratios are discussed; the 'ring currents' are useful for culculating diamagnetic anisotropies, and the sigma ratios can be converted to calculated chemical shifts by use of a previously established empirical equation. These shifts are expected to be of use in assigning signals in the experimental high-resolution P.M.R. spectra of these molecules.

The McWeeny 'ring current' theory is tested critically against a set of consistent, accurate experimental chemical shifts for 85 protons in 16 planar unsubstituted condensed benzenoid hydrocarbons, and a regression equation is derived relating quantities calculated from the theory to experimental tau values for the non-hindered protons. Systematic deviations of different types of protons from this line are discussed, as also are sigma-bond anisotropy effects and discrepancies observed for overcrowded protons. Some of the assumptions about the geometry of planar benzenoid hydrocarbons normally made in these calculations are relaxed. The McWeeny theory gives a good account of the chemical shifts of non-hindered protons in planar molecules, and the predictions of the theory are not significantly altered if the calculations are based on experimental x-ray geometry. Sigma-bond anisotropy effects are unimportant for non-hindered protons, and, at most, make only a partial contribution to the down-field shifts of hindered ones.

Second-order electric and magnetic properties calculated using an approach based upon the simultaneous analytical dependence of the bond order matrix and basis set functions on the corresponding perturbation parameters have been obtained and analyzed for a series of organic molecules. Various methods of selection of basis set quality for different atoms in investigated molecules were examined in conjunction with calculations of 1H NMR chemical shifts. Comparison of the results obtained at different levels of theory (HF, DFT, MP2) demonstrates small correlation effects for polarizability and magnetic susceptibility while the electron correlation effects play crucial role for calculations of nuclear magnetic shielding (chemical shifts).

Explicit expression derived for the first, second and third derivatives of the SCF energy with respect to parameters which can be contained both in the one electron part of the Hamiltonian and explicity in the basis functions. Several useful applications are proposed.

Chain length effects on the 1H and 13C NMR chemical shifts have been theoretically investigated for increasingly large oligomers of isotactic and syndiotactic polypropylene and poly(vinyl chloride). Chains ranging from the dimer to the octamer and decamer have been considered for polypropylene and poly(vinyl chloride), respectively. Helical structures displaying successive TG backbone conformations represent the isotactic chains, whereas syndiotactic chains are considered to be all-trans. The calculations are carried out by employing density functional theory (DFT) with the B3LYP exchange-correlation functional and the 6-311+G(2d,p) basis set.

Least‐squares representations of Slater‐type atomic orbitals as a sum of Gaussian‐type orbitals are presented. These have the special feature that common Gaussian exponents are shared between Slater‐type 2s and 2p functions. Use of these atomic orbitals in self‐consistent molecular‐orbital calculations is shown to lead to values of atomization energies, atomic populations, and electric dipole moments which converge rapidly (with increasing size of Gaussian expansion) to the values appropriate for pure Slater‐type orbitals. The ζ exponents (or scale factors) for the atomic orbitals which are optimized for a number of molecules are also shown to be nearly independent of the number of Gaussian functions. A standard set of ζ values for use in molecular calculations is suggested on the basis of this study and is shown to be adequate for the calculation of total and atomization energies, but less appropriate for studies of charge distribution.

Three basis sets (minimal s–p, extended s–p, and minimal s–p with d functions on second row atoms) are used to calculate geometries and binding energies of 24 molecules containing second row atoms. d functions are found to be essential in the description of both properties for hypervalent molecules and to be important in the calculations of two‐heavy‐atom bond lengths even for molecules of normal valence.

A complete analysis has been made for each of the high‐resolution proton magnetic resonance spectra of naphthalene, anthracene, pyrene, perylene, triphenylene, and coronene at infinite dilution in CS2 or CCl4. A partial analysis has been made for phenanthrene. The analyses yield absolute values for the chemical shifts and spin coupling constants. A correlation has been made between the π‐bond order of the particular (C☒C) bond and the spin coupling constant. Theoretical values for the ``ring current shifts'' were obtained using London type molecular orbital calculations. The agreement between experimental and theoretical values is satisfactory in that the relative positions of the proton shifts are correctly predicted in all cases.

The Hückel-London-McWeeny theory of ‘ring current’ effects on proton chemical shifts has been extended to non-planar aromatic systems. As a special case the effect of a planar ring on a generally situated proton is also treated. The predictions are compared with the experimental results on helicenes reported in Part I of this series. A satisfactory account is given of the shifts of protons primarily in the lateral deshielding regions of rings; however, shielding effects tend to be underestimated for protons situated directly above rings. For overcrowded protons an additional downfield steric effect is postulated. The theory's limitations appear to arise from the London approximation to integrals. Comparison is also made with the results of semi-classical calculations.

Fifteen procedures based on hybrid density functional theory were used to calculate magnetic properties for the carbon-bound hydrogen nuclei of 80 small to modest-sized organic molecules. The predicted isotropic shieldings derived from the various methods were compared with each other and also with solution experimental data. The computational methods investigated included the IGAIM and GIAO procedures, the 6-311++G(d,p), 6-311++G(2df,p), and 6-311++G(3df,2p) basis sets, the B3LYP, B3P86, and B3PW91 hybrid density functionals, and molecular geometries optimized using both MP2 and B3LYP methods. Although agreement with experiment consistently improved as the basis set was enlarged, the improvement upon going from 6-311++G(2df,p) to 6-311++G(3df,2p) was extremely small, and even the difference between 6-311++G(d,p) and 6-311++G(2df,p) was of a modest size. The GIAO and IGAIM procedures yielded very similar results in conjunction with the largest basis set, but GIAO suffered considerably less degradation than did IGAIM as the basis set size was decreased. The three functionals B3LYP, B3P86, and B3PW91 performed in an extremely similar fashion, although B3LYP proved marginally superior to the others. The method of geometry optimization also was found to make little difference. Of the computational methods investigated, the GIAO/B3LYP/6-311++G(d,p)//B3LYP/6-31+G(d) procedure probably represents the best compromise between accuracy and expense and yielded proton chemical shifts having a root-mean-square error of 0.15 ppm in comparison with solution experimental values after empirical linear scaling. The more expensive GIAO/B3LYP/6-311++G(2df,p)//B3LYP/6-31+G(d) method provided only a slightly lower root-mean-square error of 0.14 ppm.

Diamagnetic susceptibility exaltation, defined as the difference between the measured molar susceptibility and the susceptibility estimated neglecting the contribution of ring current, is found to be a property solely of aromatic compounds by calculating the exaltations of a wide variety of aromatic and nonaromatic hydrocarbons. Nonbenzenoid aromatic compounds exhibit exaltation, pseudoaromatic compounds do not. Exaltation is proportional to the theoretically calculated "London diamagnetism" of aromatic compounds.

A new gaussian basis set, explicity dependent on the external electric field perturbation, is proposed. The analytic form of the electric field dependence of gaussian atomic follows from a simple physical and model and the harmonic oscillator theory. These so-called electric-field-variant (EFV) orbitals are shown to form a very effective basis set for the calculation of molecular polarizabilities. The present proposal appears to circumvent serious basis set problems encountered in the molecular polarizability calculations.

Forty-five proton chemical shifts in 14 aromatic molecules have been calculated at several levels of theory: Hartree–Fock and density functional theory with several different basis sets, and also second-order Møller–Plesset (MP2) theory. To obtain consistent experimental data, the NMR spectra were remeasured on a 500 MHz spectrometer in CDCl3 solution. A set of 10 molecules without strong electron correlation effects was selected as the parametrization set. The calculated chemical shifts (relative to benzene) of 29 different protons in this set correlate very well with the experiment, and even better after linear regression. For this set, all methods perform roughly equally. The best agreement without linear regression is given by the B3LYP/TZVP method (rms deviation 0.060 ppm), although the best linear fit of the calculated shifts to experimental values is obtained for B3LYP/6-311++G**, with an rms deviation of only 0.037 ppm. Somewhat larger deviations were obtained for the second test set of 4 more difficult molecules: nitrobenzene, azulene, salicylaldehyde, and o-nitroaniline, characterized by strong electron correlation or resonance-assisted intramolecular hydrogen bonding. The results show that it is possible, at a reasonable cost, to calculate relative proton shieldings in a similar chemical environment to high accuracy. Our ultimate goal is to use calculated proton shifts to obtain constraints for local conformations in proteins; this requires a predictive accuracy of 0.1–0.2 ppm. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1887–1895, 2001

Reliability of calculated (1)H and (13)C NMR chemical shifts for various classes of organic compounds obtained with gauge-invariant atomic orbital (GIAO) approach has been studied at the PBE/3ζ level (as implemented in PRIRODA code) using linear regression analysis with experimental data. Empirical corrections for the calculated chemical shifts δ(H,calc) = δ(PBE/3ζ) - 0.08 ppm (RMS 0.18 ppm, MAD 0.66 ppm) and δ(C,calc) = δ(PBE/) (3) (ζ) - 6.35 ppm (RMS 3.09 ppm, MAD 9.42 ppm) have been developed using the sets of 263 and 308 experimental values for (1)H and (13)C chemical shifts, respectively. The confidence intervals of NMR chemical shifts at 95% confidence probability are δ(H,calc) ± 0.35 ppm for (1)H and δC,calc) ± 6.05 ppm for (13)C.

The influence of the reference standard employed in the calculation of (13)C NMR chemical shifts was investigated over a large variety of known organic compounds, using different quantum chemistry methods and basis sets. After detailed analysis of the collected data, we found that methanol and benzene are excellent reference standards for computing NMR shifts of sp(3)- and sp-sp(2)-hybridized carbon atoms, respectively. This multi-standard approach (MSTD) performs better than TMS in terms of accuracy and precision and also displays much lower dependence on the level of theory employed. The use of mPW1PW91/6-31G(d)//mPW1PW91/6-31G(d) level is recommended for accurate (13)C NMR chemical shift prediction at low computational cost.

The (13)C chemical shifts of six tertiary amines of unambiguous conformational structure are compared to predicted (13)C NMR chemical shifts obtained via empirically scaled GIAO shieldings for geometries from MM3 molecular mechanics calculations. An average deviation, absolute value of Deltadelta(av), of 0.8 ppm and a maximum deviation, absolute value of Deltadelta(max), of 2.8 ppm between predicted and experimental (13)C shifts of the six tertiary amines of unambiguous structure are found. In several cases of tertiary amines subject to rapid exchange, where experimental (13)C shifts at room temperature are weighted averages of multiple conformers, a comparison of calculated (13)C shifts of all reasonable MM3 predicted conformers with experimental (13)C shifts via a multiple independent variable regression analysis provides an efficient method of determining the major and minor conformers. The examples presented are 2-methyl-2-azabicyclo[2.2.1]heptane and 1,6-diazabicyclo[4.3.1]decane, which each have two expected contributing structures, and 2-(diethylamino)propane and 1,8-diazabicyclo[6.3.1]dodecane, where ten and seven low-energy conformers, respectively, are predicted by MM3 calculations.

Proton chemical shifts of eight cyclic amide molecules were measured in DMSO and D2O solutions. The magnetic shieldings of the corresponding aliphatic, aromatic, and amide protons were calculated by Hartree-Fock and DFT, using the 6-311G**, 6-311++G**, and TZVP basis sets. For aliphatic protons, all of these methods reproduce the experimental values in DMSO solutions excellently after linear regression. The Hartree-Fock method tends to give slightly better agreement than DFT. The best performance is given by the HF/6-311G** method, with an rms deviation of 0.068 ppm. The deviations from experimental chemical shifts in D2O solutions are only slightly larger than those in DMSO solutions. This suggests that we can use the calculated gas phase proton chemical shifts directly to predict experimental data in various solvents, including water. For amide protons, which exchange with water and form hydrogen bonds with DMSO, only modest agreement is obtained, as expected. The present studies confirm that the GIAO approach can reach high accuracy for the relative chemical shifts of aliphatic and aromatic protons at a low cost. Such calculations may provide constraints for the conformational analysis of proteins and other macromolecules.

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