Prashant Uday Manohar

A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions

A noniterative N (7) triples correction for the equation-of-motion coupled-cluster method with single and double substitutions (CCSD) is presented. The correction is derived by second-order perturbation treatment of the similarity-transformed CCSD Hamiltonian. The spin-conserving variant of the correction is identical to the triples correction of Piecuch and co-workers [Mol. Phys. 104, 2149 (2006)] derived within method-of-moments framework and is not size intensive. The spin-flip variant of the correction is size intensive. The performance of the correction is demonstrated by calculations of electronic excitation energies in methylene, nitrenium ion, cyclobutadiene, ortho-, meta-, and para-benzynes, 1,2,3-tridehydrobenzene, as well as C-C bond breaking in ethane. In all cases except cyclobutadiene, the absolute values of the correction for energy differences were 0.1 eV or less. In cyclobutadiene, the absolute values of the correction were as large as 0.4 eV. In most cases, the correction reduced the errors against the benchmark values by about a factor of 2-3, the absolute errors being less than 0.04 eV.

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.

Perturbative triples correction for the equation-of-motion coupled-cluster wave functions with single and double substitutions for ionized states: Theory, implementation, and examples

A noniterative N(6) triples energy correction is presented for the equation-of-motion coupled-cluster method with single and double substitutions for ionized states (EOM-IP-CCSD). The correction, which is size intensive, is derived using a second-order Rayleigh-Schrodinger perturbative treatment and is similar to the approach of Stanton and Gauss [Theor. Chim. Acta 93, 303 (1996)]. In the present implementation, only the target EOM-IP states are corrected, and the reference state is described by CCSD; the method is therefore more useful for the study of the target states themselves than ionization potentials. The performance of the correction, which demonstrates the caveat above, is demonstrated by applications to singlet methylene, BNB(-), nitrogen, carbon monoxide, acetylene, benzene, thymine, and adenine.

First- and second-order electrical properties computed at the FSMRCCSD level for excited states of closed-shell molecules using the constrained-variational approach

Fock space multireference coupled-cluster (FSMRCC) method emerged as an efficient tool to describe the electronic structure of nearly degenerate cases. Development of linear response has been one of the challenging problems in FSMRCC due to the multiple-root nature of the effective Hamiltonian. A response from any of the roots would span the space for getting the properties. Hence, all roots perturbed by the external field would proliferate the excited states. We recently developed the FSMRCC method for the efficient evaluation of analytic response properties using a constrained variation approach. In this paper, we present analytic dipole moments and polarizabilities of H(2)O, O(3), and CH(+) molecules in low-lying excited states along with brief discussion of singlet triplet decoupling of (1,1) sector of FSMRCC resulting from spin adaptation.

Effect of a Heteroatom on Bonding Patterns and Triradical Stabilization Energies of 2,4,6-Tridehydropyridine versus 1,3,5-Tridehydrobenzene

Electronic structure of 2,4,6-tridehydropyridine and isoelectronic 1,3,5-tridehydrobenzene is characterized by the equation-of-motion spin-flip coupled-cluster calculations with single and double substitutions and including perturbative triple corrections. Equilibrium geometries of the three lowest electronic states, vertical and adiabatic states ordering, and triradical stabilization energies are reported for both triradicals. In 1,3,5-tridehydrobenzene, the ground (2)A(1) state is 0.016 eV below the (2)B(2) state, whereas in 2,4,6-tridehydropyridine the heteroatom reverses adiabatic state ordering bringing (2)B(2) below (2)A(1) by 0.613 eV. The adiabatic doublet-quartet gap of 2,4,6-tridehydropyridine is smaller than that of 1,3,5-tridehydrobenzene by 0.08 eV; the respective values are 1.223 and 1.302 [corrected] eV. Moreover, the heteroatom reduces bonding interactions between the C(2) and C(6) radical centers, which results in the increased stabilizing interactions between C(4) and C(2)/C(6). Triradical stabilization energies corresponding to the separation of C(4) and C(2) are 19.7 and -0.2 kcal/mol, respectively, in contrast to 2.8 kcal/mol in 1,3,5-tridehydrobenzene. Similarly weak interactions between C(2) and C(6) are also observed in 2,6-didehydropyridine resulting in a nearly zero singlet-triplet energy gap, in contrast to m-benzyne and 2,4-didehydropyridine. The total interaction energy of the three radical centers is very similar in 1,3,5-tridehydrobenzene and 2,4,6-tridehydropyridine and is 19.5 and 20.1 kcal/mol, respectively.

Analytical Dipole Moments and Dipole Polarizabilities of Oxygen Mono-Fluoride and Nitrogen Dioxide: A Constrained Variational Response to Fock-Space Multi-Reference Coupled-Cluster Method

In this article, we present analytical dipole moments and dipole polarizabilities of oxygen monofluoride and nitrogen dioxide using the recently developed constrained variational approach in Fock-space multi-reference coupled-cluster singles and doubles (CVA-FSMRCCSD) method. Both these molecules are important in atmospheric chemistry. The near-degeneracy in low-lying states of these molecules demands for MR description of the wavefunction. We also report our study of variation in the properties of oxygen monofluoride with respect to basis set. Benchmark results, wherever available, have been duly reported for comparison.

Constrained Variational Response to Fock‐Space Multi‐Reference Coupled‐Cluster Theory: Formulation for Excited‐State Electronic Structure Calculations and Some Pilot Applications

Fock‐space (FS) multi‐reference (MR) coupled‐cluster (CC) method has emerged as compact tool to account for electronic structure of open‐shell systems and molecules in low‐lying excited states. Development of linear response (LR) has been one of the challenging problems in FSMRCC due to multiple‐root nature of effective Hamiltonian. The recently developed constrained variational approach (CVA) has opened up a promising tool for efficient evaluation of analytic response properties. In this article, we present formulation of the method for excited state calculations. We discuss the decoupling of equations as a result of spin‐adaptation and present some preliminary results for analytical dipole moments and polarizabilities of some molecules in low‐lying triplet excited states.

On Some Aspects of Fock-Space Multi-Reference Coupled-Cluster Singles and Doubles Energies and Optical Properties

Multi-reference coupled cluster methods are established as accurate and efficient tools for describing electronic structure of quasi degenerate states. Recently we have developed multi-reference coupled cluster linear response approach based on the constrained variation method. The method is very general and can describe challenging problems due to the multiple-root nature of effective Hamiltonian. Calculation of response properties for the ionized/electron attached or excited state molecules is a challenging task. With this formulation it is possible to accurately predict the higher order molecular properties of the open shell molecules. In this article we review the response approaches for quasi degenerate cases with emphasis on Fock space multi-reference coupled cluster method.

Resolution of the Identity and Cholesky Representation of EOM-MP2 Approximation: Implementation, Accuracy and Efficiency

We present a Resolution of Identity and Cholesky Decomposition Based Implementation of EOM-MP2 approximation. The RI and CD based EOM-MP2 shows significant speed-up and less storage requirement than the conventional canonical version and can be applied to very large systems. The new algorithm used for this implementation eliminates the most storage requiring four-index quantities resulting in the decrease of storage requirement, reduction in I/O penalties and improved parallel performance, at the expense of more floating point operations. Therefore, the speed-up compared to conventional EOM-MP2 method is more prominent in case of EA, EE and SF case where the storage bottleneck is significant than the EOM-IP-MP2 method, where the storage requirement is significantly less. However, the RI/CD based EOM-IP-MP2 can be coupled with frozen natural orbitals to gain further speed-up.Graphical AbstractSynopsis: We present RI/CD implementation on EOM-MP2 method for computing IP, EA, EE and SF target electronic states of molecules. The RI/CD implementation results in speed-up in computational time and reduction in storage requirements without much compromise on accuracy, thereby widening the applicability of the method to molecules of bigger computional size.