Dmitry Zuev

New implementation of high‐level correlated methods using a general block tensor library for high‐performance electronic structure calculations

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.

Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks

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.

General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks

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.

A Fresh Look at Resonances and Complex Absorbing Potentials: Density Matrix-Based Approach.

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.

Complex-scaled equation-of-motion coupled-cluster method with single and double substitutions for autoionizing excited states: theory, implementation, and examples.

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.

Electronic structure of the two isomers of the anionic form of p-coumaric acid chromophore

A theoretical study of the electronic structure of the photoactive yellow protein (PYP) model chromophore, para-coumaric acid (p-CA), is presented. Electronically excited states of the phenolate and carboxylate isomers of the deprotonated p-CA are characterized by high-level ab initio methods including state-specific and multistate multireference pertrubation theory (SS-CASPT2, and MS-CASPT2), equation-of-motion coupled-cluster methods with single and double substitutions (EOM-CCSD) and with an approximate account of triple excitations (CC3). We found that the two isomers have distinctly different patterns of ionization and excitation energies. Their excitation energies differ by more than 1 eV, in contradiction to the experimental report [Rocha-Rinza et al., J. Phys. Chem. A 113, 9442 (2009)]. The calculations confirm metastable (autoionizing) character of the valence excited states of both phenolate and carboxylate isomers of p-CA(-) in the gas phase. The type of resonance is different in the two forms. In the phenolate, the excited state lies above the detachment continuum (a shape resonance), whereas in the carboxylate the excited π→π(*) state lies below the π-orbital ionization continuum, but is above the states derived from ionization from three other orbitals (Feshbach resonance). The computed oscillator strength of the bright electronic state in the phenolate is higher than in the carboxylate, in agreement with Hückels model predictions. The analysis of photofragmentation channels shows that the most probable products for the methylated derivatives of the phenolate and carboxylate forms of p-CA(-) are CH(3), CH(2)O and CH(3), CH(2)O, CO(2), respectively, thus suggesting an experimental probe that may discriminate between the two isomers.

Effect of microhydration on the electronic structure of the chromophores of the photoactive yellow and green fluorescent proteins

Electronic structure calculations of microhydrated model chromophores (in their deprotonated anionic forms) of the photoactive yellow and green fluorescent proteins (PYP and GFP) are reported. Electron-detachment and excitation energies as well as binding energies of mono- and dihydrated isomers are computed and analyzed. Microhydration has different effects on the excited and ionized states. In lower-energy planar isomers, the interaction with one water molecule blueshifts the excitation energies by 0.1-0.2 eV, whereas the detachment energies increase by 0.4-0.8 eV. The important consequence is that microhydration by just one water molecule converts the resonance (autoionizing) excited states of the bare chromophores into bound states. In the lower-energy microhydrated clusters, interactions with water have negligible effect on the chromophore geometry; however, we also identified higher-energy dihydrated clusters of PYP in which two water molecules form hydrogen-bonding network connecting the carboxylate and phenolate moieties and the chromophore is strongly distorted resulting in a significant shift of excitation energies (up to 0.6 eV).

New algorithms for iterative matrix-free eigensolvers in quantum chemistry

New algorithms for iterative diagonalization procedures that solve for a small set of eigen‐states of a large matrix are described. The performance of the algorithms is illustrated by calculations of low and high‐lying ionized and electronically excited states using equation‐of‐motion coupled‐cluster methods with single and double substitutions (EOM‐IP‐CCSD and EOM‐EE‐CCSD). We present two algorithms suitable for calculating excited states that are close to a specified energy shift (interior eigenvalues). One solver is based on the Davidson algorithm, a diagonalization procedure commonly used in quantum‐chemical calculations. The second is a recently developed solver, called the “Generalized Preconditioned Locally Harmonic Residual (GPLHR) method.” We also present a modification of the Davidson procedure that allows one to solve for a specific transition. The details of the algorithms, their computational scaling, and memory requirements are described. The new algorithms are implemented within the EOM‐CC suite of methods in the Q‐Chem electronic structure program.

Erratum: "Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks" [J. Chem. Phys. 141, 024102 (2014)].

Author(s): Zuev, Dmitry; Jagau, Thomas-C; Bravaya, Ksenia B; Epifanovsky, Evgeny; Shao, Yihan; Sundstrom, Eric; Head-Gordon, Martin; Krylov, Anna I

Correction to "A Fresh Look at Resonances and Complex Absorbing Potentials: Density Matrix-Based Approach".

J. Phys. Chem. Lett. 2014, 5, 310−315, 10.1021/jz402482a I Table 1, the experimental value for the width of the Π resonance of CO− taken from ref 1 is in fact a half-width. Thus, the corresponding entry in Table 1 should read 0.8 eV and not 0.4 eV. Although this correction does not affect the main conclusions of the paper, the agreement of the theoretical values for the resonance width computed with our approach (CAP-EOM-EA-CCSD) with the corrected experimental value is unsatisfactory. This is likely due to using an insufficient basis set as further computations illustrate. The reference value for the Πg resonance of N2 has been taken from ref 3 and is not affected.