[Show abstract][Hide abstract] ABSTRACT: We present a formalism and an implementation for calculating spin-orbit couplings
(SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
The Journal of Chemical Physics 08/2015; 143(6):064102. DOI:10.1063/1.4927785 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An efficient new molecular orbital (MO) basis algorithm is reported implementing the pair atomic resolution of the identity approximation (PARI) to evaluate the exact exchange contribution (K) to self-consistent field methods, such as hybrid and range-separated hybrid density functionals. The PARI approximation, in which atomic orbital (AO) basis function pairs are expanded using auxiliary basis functions centered only on their two respective atoms, was recently investigated by Merlot et al. [J. Comput. Chem. 2013, 34, 1486]. Our algorithm is significantly faster than quartic scaling RI-K, with an asymptotic exchange speedup for hybrid functionals of (1 + X/N), where N and X are the AO and auxiliary basis dimensions. The asymptotic speedup is 2 + 2X/N for range separated hybrids such as CAM-B3LYP, ωB97X-D, and ωB97X-V which include short- and long-range exact exchange. The observed speedup for exchange in ωB97X-V for a C68 graphene fragment in the cc-pVTZ basis is 3.4 relative to RI-K. Like conventional RI-K, our method greatly outperforms conventional integral evaluation in large basis sets; a speedup of 19 is obtained in the cc-pVQZ basis on a C54 graphene fragment. Negligible loss of accuracy relative to exact integral evaluation is demonstrated on databases of bonded and nonbonded interactions. We also demonstrate both analytically and numerically that the PARI-K approximation is variationally stable.
Journal of Chemical Theory and Computation 02/2015; 11(2):518-527. DOI:10.1021/ct5008586 · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
[Show abstract][Hide abstract] ABSTRACT: A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π(*) shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.
The Journal of Chemical Physics 07/2014; 141(2):024102. DOI:10.1063/1.4885056 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The development of reliable theoretical methods and the provision of efficient computer programs for the investigation of optical spectra and photochemistry of large molecules in general is one of the most important tasks of contemporary theoretical chemistry. Here, we present an overview of the current features of our implementation of the algebraic diagrammatic construction scheme of the polarisation propagator, which is a versatile and robust approach for the theoretical investigation of excited states and their properties.
[Show abstract][Hide abstract] ABSTRACT: A new strategy of using complex absorbing potentials (CAPs) within electronic structure calculations of metastable electronic states, which are ubiquitous in chemistry and physics, is presented. The stumbling block in numerical applications of CAPs is the necessity to optimize the CAP strength for each system, state, and one-electron basis set, while there is no clear metric to assess the quality of the results and no simple algorithm of achieving numerical convergence. By analyzing the behavior of resonance wave functions, we found that robust results can be obtained when considering fully stabilized resonance states characterized by constant density at large η (parameter determining the CAP strength). Then the perturbation due to the finite-strength CAP can be removed by a simple energy correction derived from energy decomposition analysis and response theory. The utility of this approach is illustrated by CAP-augmented calculations of several shape resonances using EOM-EA-CCSD with standard Gaussian basis sets.
[Show abstract][Hide abstract] ABSTRACT: We present a general implementation of the resolution-of-the-identity (RI) and Cholesky decomposition (CD) representations of electron repulsion integrals within the coupled-cluster with single and double substitutions (CCSD) and equation-of-motion (EOM) family of methods. The CCSD and EOM-CCSD equations are rewritten to eliminate the storage of the largest four-index intermediates leading to a significant reduction in disk storage requirements, reduced I/O penalties, and, as a result, improved parallel performance. In CCSD, the number of rate-determining contractions is also reduced; however, in EOM the number of operations is increased because the transformed integrals, which are computed once in the canonical implementation, need to be reassembled at each Davidson iteration. Nevertheless, for large jobs the effect of the increased number of rate-determining contractions is surpassed by the significantly reduced memory and disk usage leading to a considerable speed-up. Overall, for medium-size examples, RI/CD CCSD calculations are approximately 40% faster compared with the canonical implementation, whereas timings of EOM calculations are reduced by a factor of two. More significant speed-ups are obtained in larger bases, i.e., more than a two-fold speed-up for CCSD and almost five-fold speed-up for EOM-EE-CCSD in cc-pVTZ. Even more considerable speedups (6-7-fold) are achieved by combining RI/CD with the frozen natural orbitals approach. The numeric accuracy of RI/CD approaches is benchmarked with an emphasis on energy differences. Errors in EOM excitation, ionization, and electron-attachment energies are less than 0.001 eV with typical RI bases and with a 10(-4) threshold in CD. Errors with 10(-2) and 10(-3) thresholds, which afford more significant computational savings, are less than 0.04 and 0.008 eV, respectively.
The Journal of Chemical Physics 10/2013; 139(13):134105. DOI:10.1063/1.4820484 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This article presents an open-source object-oriented C++ library of classes and routines to perform tensor algebra.The primary purpose of the library is to enable post-Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide-and-conquer-type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q-Chem electronic structure software uses this library to drive coupled-cluster, equation-of-motion, and algebraic-diagrammatic construction methods.
[Show abstract][Hide abstract] ABSTRACT: Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H(-), and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, θ. Standard basis sets that are optimized for not-complex-scaled calculations (θ = 0) are not sufficiently flexible to describe the θ-dependence of the wave functions even when heavily augmented by additional sets.
The Journal of Chemical Physics 03/2013; 138(12):124106. DOI:10.1063/1.4795750 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This work reports refinements of the energetic ordering of the known low-energy structures of sulphate–water clusters SO_{4}^{2-}(H_{2}O)_{n} (n = 3–6) using high-level electronic structure methods. Coupled cluster singles and doubles with perturbative triples (CCSD(T)) is used in combination with an estimate of basis set effects up to the complete basis set limit using second-order Møller–Plesset theory. Harmonic zero-point energy (ZPE), included at the B3LYP/6-311 + + G(3df,3pd) level, was found to have a significant effect on the energetic ordering. In fact, we show that the energetic ordering is a result of a delicate balance between the electronic and vibrational energies. Limitations of the ZPE calculations, both due to electronic structure errors, and use of the harmonic approximation, probably constitute the largest remaining errors. Due to the often small energy differences between cluster isomers, and the significant role of ZPE, deuteration can alter the relative energies of low-lying structures, and, when it is applied in conjunction with calculated harmonic ZPEs, even alters the global minimum for n = 5. Experiments on deuterated clusters, as well as more sophisticated vibrational calculations, may therefore be quite interesting.
[Show abstract][Hide abstract] ABSTRACT: Benchmark calculations of the lowest ionized state of the (A:T)(2) (mixed adenine thymine) cluster at the geometry taken from the DNA X-ray structure are presented. Vertical ionization energies (IEs) computed by the equation-of-motion coupled-cluster method with single and double substitutions are reported and analyzed. The shift in IE relative to the monomer (A) is -0.7 eV. The performance of the widely used B3LYP, omega B97X-D, and M06-2X functionals with respect to their ability to describe energetics and the character (localization versus delocalization) of the ionized states is also investigated. The shifts in IEs caused by H-bonding and stacking interactions are analyzed in terms of additive versus cooperative effects. It is found that the cooperative effect accounts for more than 20% of the shift in IE relative to the monomer. The cooperative effect and, consequently, the magnitude of the shift are well reproduced by the hybrid quantum mechanics/molecular mechanics scheme in which neutral thymine bases are represented by point charges.
[Show abstract][Hide abstract] ABSTRACT: The gas-phase reaction of benzene with O((3)P) is of considerable interest for modeling of aromatic oxidation, and also because there exist fundamental questions concerning the prominence of intersystem crossing in the reaction. While its overall rate constant has been studied extensively, there are still significant uncertainties in the product distribution. The reaction proceeds mainly through the addition of the O atom to benzene, forming an initial triplet diradical adduct, which can either dissociate to form the phenoxy radical and H atom or undergo intersystem crossing onto a singlet surface, followed by a multiplicity of internal isomerizations, leading to several possible reaction products. In this work, we examined the product branching ratios of the reaction between benzene and O((3)P) over the temperature range 300-1000 K and pressure range 1-10 Torr. The reactions were initiated by pulsed-laser photolysis of NO(2) in the presence of benzene and helium buffer in a slow-flow reactor, and reaction products were identified by using the multiplexed chemical kinetics photoionization mass spectrometer operating at the Advanced Light Source (ALS) of Lawrence Berkeley National Laboratory. Phenol and phenoxy radical were detected and quantified. Cyclopentadiene and cyclopentadienyl radical were directly identified for the first time. Finally, ab initio calculations and master equation/RRKM modeling were used to reproduce the experimental branching ratios, yielding pressure-dependent rate expressions for the reaction channels, including phenoxy + H, phenol, cyclopentadiene + CO, which are proposed for kinetic modeling of benzene oxidation.
The Journal of Physical Chemistry A 03/2010; 114(9):3355-70. DOI:10.1021/jp9114145 · 2.69 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Electronic structure calculations of the singly and doubly ionized states of deprotonated 4(')-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI anion) are presented. One-electron oxidation produces a doublet radical that has blueshifted absorption, whereas the detachment of two electrons yields a closed-shell cation with strongly redshifted (by about 0.6 eV) absorption relative to the HBDI anion. The results suggest that the doubly oxidized species may be responsible for oxidative redding of green fluorescent protein. The proposed mechanism involves two-step oxidation via electronically excited states and is consistent with the available experimental information [A. M. Bogdanov, A. S. Mishin, I. V. Yampolsky, et al., Nat. Chem. Biol. 5, 459 (2009)]. The spectroscopic signatures of the ionization-induced structural changes in the chromophore are also discussed.
The Journal of Chemical Physics 03/2010; 132(11):115104. DOI:10.1063/1.3336425 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present quantum chemical calculations of the properties of the anionic form of the green fluorescent protein (GFP) chromophore that can be directly compared to the results of experimental measurements: the cis-trans isomerization energy profile in water. Calculations of the cis-trans chromophore isomerization pathway in the gas phase and in water reveal a problematic behavior of density functional theory and scaled opposite-spin-MP2 due to the multiconfigurational character of the wave function at twisted geometries. The solvent effects treated with the continuum solvation models, as well as with the water cluster model, are found to be important and can reduce the activation energy by more than 10 kcal/mol. Strong solvent effects are explained by the change in charge localization patterns along the isomerization coordinate. At the equilibrium, the negative charge is almost equally delocalized between the phenyl and imidazolin rings due to the interaction of two resonance structures, whereas at the transition state the charge is localized on the imidazolin moiety. Our best estimate of the barrier obtained in cluster calculations employing the effective fragment potential-based quantum mechanics/molecular mechanics method with the complete active space self-consistent field description of the chromophore augmented by perturbation theory correction and the TIP3P water model is 14.8 kcal/mol, which is in excellent agreement with the experimental value of 15.4 kcal/mol. This result helps to resolve previously reported disagreements between experimental measurements and theoretical estimates.
Journal of Chemical Theory and Computation 07/2009; 5(7). DOI:10.1021/ct9001448 · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present the results of quantum chemical calculations of the electronic properties of the anionic form of the green fluorescent protein chromophore in the gas phase. The vertical detachment energy of the chromophore is found to be 2.4−2.5 eV, which is below the strongly absorbing ππ* state at 2.6 eV. The vertical excitation of the lowest triplet state is around 1.9 eV, which is below the photodetachment continuum. Thus, the lowest bright singlet state is a resonance state embedded in the photodetachment continuum, whereas the lowest triplet state is a regular bound state. Based on our estimation of the vertical detachment energy, we attribute a minor feature in the action spectrum as due to the photodetachment transition. The benchmark results for the bright ππ* state demonstrated that the scaled opposite-spin method yields vertical excitation within 0.1 eV (20 nm) from the experimental maximum at 2.59 eV (479 nm). We also report estimations of the vertical excitation energy obtained with the equation-of-motion coupled cluster with the singles and doubles method, a multireference perturbation theory corrected approach MRMP2 as well as the time-dependent density functional theory with range-separated functionals. Expanding the basis set with diffuse functions lowers the ππ* vertical excitation energy by 0.1 eV at the same time revealing a continuum of “ionized” states, which embeds the bright ππ* transition.
Journal of Chemical Theory and Computation 07/2009; 5(7). DOI:10.1021/ct900143j · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Non-adiabatic and spin-forbidden processes involve transitions between electronic states through potential energy surface (PES) crossings. They are often found in atmospheric and combustion chemistry, photochemistry and photobiology. To describe the kinetics of such processes, a version of transition state theory can be applied. Locating the minimum energy crossing point of the PESs is the first step of characterizing a spin-forbidden reaction. The point corresponds to the transition state of the process. This work presents a computational procedure for minimizing singlet-triplet crossings of PESs, which is applied to a benchmark series of methylene-related radicals, formaldehyde, and oxybenzene, an intermediate in atmospheric formation of phenol. The intersection minimum in the studied methylene-related radicals is located very close to the excited state minimum, singlet for CH_2 and triplet for CHF and CF_2. The crossing in oxybenzene is found along the CO wagging coordinate. In the case of para-benzyne, which has a singlet-triplet adiabatic excitation energy of less than 0.2 eV, the crossing minimum is unexpectedly located 0.65 eV above the ground state equilibrium energy and corresponds to a distorted ring geometry.
[Show abstract][Hide abstract] ABSTRACT: The photodissociation dynamics of H(2)CO is known to involve electronic states S(1), T(1) and S(0). Recent quasiclassical trajectory (QCT) calculations, in conjunction with experiment, have identified a "roaming" H-atom pathway to the molecular products, H(2)+CO [Townsend; et al. Science 2004, 306, 1158.]. These calculations were initiated at the global minimum (GM) of S(0), which is where the initial wave function is located. The "roaming" mechanism is not seen if trajectories are initiated from the molecular transition state saddle point (SP). In this Letter we identify the minimum energy-crossing configurations and energy of the T(1)/S(0) potentials as a step toward studying the multisurface nature of the photodissociation. QCT calculations are initiated at these configurations on a revised potential energy surface and the results are compared to those initiated, as previously, from the S(0) GM as well as the S(0) SP. The product state distributions of H(2) + CO from trajectories initiated at the T(1)/S(0) crossing are in excellent agreement with those initiated at the S(0) GM.
The Journal of Physical Chemistry A 12/2008; 112(51):13267-70. DOI:10.1021/jp808410p · 2.69 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An implementation of the projected gradient method for locating the minimum energy crossing point between electronic states of different symmetry/multiplicity within the equation-of-motion coupled-cluster family of methods is reported. The method is applied to characterize the intersections between electronic states in N þ 3 , NO 2 , and para-benzyne using the excitation energies, ionization potential, and spin-flip variants of the equation-of-motion coupled-cluster methods. The performance of the algorithm is discussed and recommendations for improving the convergence in problematic situations are given.
[Show abstract][Hide abstract] ABSTRACT: Vertical excitation energies in uracil in the gas phase and in water solution are investigated by the equation-of-motion coupled-cluster and multireference configuration interaction methods. Basis set effects are found to be important for converged results. The analysis of electronic wave functions reveals that the lowest singlet states are predominantly of a singly excited character and are therefore well described by single-reference equation-of-motion methods augmented by a perturbative triples correction to account for dynamical correlation.Our best estimates for the vertical excitation energies for the lowest singlet n --> pi* and pi --> pi* are 5.0 +/- 0.1 eV and 5.3 +/- 0.1 eV, respectively. The solvent effects for these states are estimated to be +0.5 eV and +/- 0.1 eV, respectively. We attribute the difference between the computed vertical excitations and the maximum of the experimental absorption to strong vibronic interaction between the lowest A" and A' states leading to intensity borrowing by the forbidden transition.
The Journal of Physical Chemistry A 10/2008; 112(40):9983-92. DOI:10.1021/jp803758q · 2.69 Impact Factor