Multireference space without first solving the configuration interaction problem

We further develop an idea to generate a compact multireference space without first solving the configuration interaction problem previously proposed for the ground state (GS) (Glushkov, Chem. Phys. Lett. 1995, 244, 1). In the present contribution, our attention is focused on low‐lying excited states (ESs) with the same symmetry as the GS which can be adequately described in terms of an high‐spin open‐shell formalism. Two references Møller–Plesset (MP) like perturbation theory for ESs is developed. It is based on: (1) a main reference configuration constructed from the parent molecular orbitals adjusted to a given ES and (2) secondary double excitation configuration built on the GS like orbitals determined by the Hartree–Fock equations subject to some orthogonality constraints. It is shown how to modify the MP zeroth‐order Hamiltonian so that the reference configurations and corresponding excitations are eigenfunctions of it and are compatible with orthogonality conditions for the GS and ES. Intruder states appearance is also discussed. The proposed scheme is applied to the GS, ES, and excitation energies of small molecules to illustrate and calibrate our calculations. © 2013 Wiley Periodicals, Inc.     

Parallel internally contracted multireference configuration interaction

A parallel implementation of the internally contracted (IC) multireference configuration (MRCI) module of the MOLPRO quantum chemistry program is described. The global array (GA) toolkit has been used in order to map an existing disk-paging small-memory algorithm onto a massively parallel supercomputer, where disk storage is replaced by the combined memory of all processors. This model has enabled a rather complicated code to be ported to the parallel environment without the need for the wholesale redesign of algorithms and data structures. Examples show that the parallel ICMRCI program can deliver results in a fraction of the time needed for equivalent uncontracted MRCI computations. Further examples demonstrate that ICMRCI computations with up to 10⁷ variational parameters, and equivalent to uncontracted MRCI with 10⁹ configurations, are feasible. The largest calculation demonstrates a parallel efficiency of about 80% on 128 nodes of a Cray T3E-300. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1215–1228, 1998     

The quest for best suited references for configuration interaction singles calculations of core excited states

Near edge X‐ray absorption fine structure (NEXAFS) simulations based on the conventional configuration interaction singles (CIS) lead to excitation energies, which are systematically blue shifted. Using a (restricted) open shell core hole reference instead of the Hartree Fock (HF) ground state orbitals improves (Decleva et al., Chem. Phys., 1992, 168, 51) excitation energies and the shape of the spectra significantly. In this work, we systematically vary the underlying SCF approaches, that is, based on HF or density functional theory, to identify best suited reference orbitals using a series of small test molecules. We compare the energies of the K edges and NEXAFS spectra to experimental data. The main improvement compared to conventional CIS, that is, using HF ground state orbitals, is due to the electrostatic influence of the core hole. Different SCF approaches, density functionals, or the use of fractional occupations lead only to comparably small changes. Furthermore, to account for bigger systems, we adapt the core‐valence separation for our approach. We demonstrate that the good quality of the spectrum is not influenced by this approximation when used together with the non‐separated ground state wave function. Simultaneously, the computational demands are reduced remarkably. © 2016 Wiley Periodicals, Inc.     

Evaluation of the restricted virtual space approximation in the algebraic‐diagrammatic construction scheme for the polarization propagator to speed‐up excited‐state calculations

The applicability and limitations of the restricted virtual space (RVS) approximation within the algebraic‐diagrammatic construction (ADC) scheme for the polarization propagator up to third order is evaluated. In RVS‐ADC, not only the core but also a substantial amount of energetically high‐lying virtual orbitals is restricted in excitation energy calculations of low‐lying excited electronic states. Using octatetraene, indole, and pyridine as representative examples and different standard basis sets of triple‐zeta quality, RVS‐ADC(2) turns out to be highly useful and to have negligible effects on ππ* excited states. However, for nπ* or πσ* states, the RVS approximation is generally less reliable but better at third‐order than second‐order ADC level. In addition, a unified, basis‐set independent, thus normalized virtual orbital threshold (value) is introduced, making the RVS approximation more controllable and a priori applicable. © 2017 Wiley Periodicals, Inc.     

Conical Intersections and Low‐Lying Electronic States of Tetrafluoroethylene

The low‐lying electronic states of tetrafluoroethylene (C₂F₄) are characterized theoretically for the first time using equation‐of‐motion coupled cluster theory (EOM‐CCSD), and complete active space self‐consistent field (CASSCF) and second‐order perturbation theory (CASPT2). Computations are performed for vertical excitation energies, equilibrium geometries, minimum‐energy conical intersections, and potential energy curves along three geometric coordinates: 1) twisting of the F?C?C?F dihedral angle, 2) pyramidalization of the CF₂ group, and 3) migration of a fluorine atom resulting in an ethylidene‐like (CF₃CF) structure. The results suggest two relaxation pathways from the Rydberg‐3s excited electronic state to the ground state. These relaxation pathways are discussed in conjunction with the femtosecond photoionization spectroscopy results of Trushin et al. [ChemPhysChem­ 2004 , 5, 1389].     

Theoretical Approach Towards the Understanding of Asymmetric Additions of Dialkylzinc to Enals and Iminals Catalysed by [2.2]Paracyclophane‐Based N,O‐Ligands

The 1,2‐ and 1,4‐asymmetric additions of dialkylzinc reagents (ZnMe₂ and ZnEt₂) to cinnamaldehyde and N‐formylbenzylimine catalysed by [2.2]paracyclophane‐based N,O‐ligands were studied with quantum chemical methods. High level LPNO‐CEPA/1 (local pair natural orbital coupled electron pair approximation 1) calculations were performed to obtain reliable reaction barriers and binding energies. The calculations supported the experimentally observed selectivities. In the reaction, the alkyl transfer takes place on a binuclear zinc complex. Regioselectivity can be traced back to changes in π‐conjugation. Because the less conjugated N‐formylbenzylimine is more flexible, it is better suited for 1,4‐additions. Moreover, bulky ligands were shown to be important for stereoselectivity. The reason is that the tricyclic motif present in the transition states is sterically less hindered in the anti conformation. Based on the LPNO‐CEPA/1 data, a set of popular theoretical methods are validated. Although it was possible to set up a procedure to obtain the stereoselectivities with computationally less demanding methods, this was not possible for the regioselectivity of the reactions.     

Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The Role of the nπ* 1Au State in the Photoabsorption and Relaxation of Pyrazine

The geometric, energetic, and spectroscopic properties of the ground state and the lowest four singlet excited states of pyrazine have been studied by using DFT/TD‐DFT, CASSCF, CASPT2, and related quantum chemical calculations. The second singlet nπ* state, ¹A_u, which is conventionally regarded dark due to the dipole‐forbidden ¹A_u←¹A_g transition, has been investigated in detail. Our new simulation has shown that the state could be visible in the absorption spectrum by intensity borrowing from neighboring nπ* ¹B_3u and ππ* ¹B_2u states through vibronic coupling. The scans on potential‐energy surfaces further indicated that the ¹A_u state intersects with the ¹B_2u states near the equilibrium of the latter, thus implying its participation in the ultrafast relaxation process.     

Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications.

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.     

A comparative multi-reference configuration interaction study of the low-lying states of two thione isomers of thiophenol

Multi-reference configuration interaction, MR-CI (including extensivity corrections, named +Q), calculations were performed on the S₀–S₃ states of cyclohexa-2,4-diene-1-thione (thione 24 ) and cyclohexa-2,5-diene-1-thione (thione 25 ), which are thione isomers of thiophenol. Several types of uncontracted MR-CIS and MR-CISD wavefunctions were employed, comprising MR-CI expansions as large as ~365 × 10⁶ configuration state functions. The nature of the studied excited states was characterized. Vertical excitation energies (ΔE) and oscillator strengths (f) were computed. The most intense transitions (S₀ → S₂ for 24 and S₀ → S₃ for 25 ) did not change with the wavefunction, although a variation as large as ~1 eV was obtained for the S₃ state of 24 , at the highest (MR-CI+Q) level. On the other hand, ΔE changed at most by ~0.56 eV for 25 as the wavefunction changes, at the same level. The S₁ state of both thiones was found to have nπ* character and is in the visible region. For 24 , S₂ and S₃ are ππ* and nπ* states, respectively, while for 25 the reverse order is obtained. S₂ and S₃ are in the range ~3.5 to 5.2 eV, again at the highest level. It is the first time that the excited states of the title molecules are studied. The computed results agree with the experimental onset of photoreactions of thiones 24 and 25 found by Reva et al (Phys. Chem. Chem. Phys., 2015 , 17, 4888).     

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. © 2013 Wiley Periodicals, Inc.     

Spin Flip Models in the Spin Coupling Method of Many-Particle Amplitudes

A special class of models is presented in which correlation effects for quasidegenerate electronic states are calculated without resorting to complete MRCI schemes. The high-spin reference determinant is transformed into the desired low-spin state by the spin flip procedure with concomitant electron elimination or addition. For the given spin flip process, variational equations that define the corresponding spin coupling matrix have been obtained. For the simplest spin flip model presented by A. Krylova as the SF-CIS method, a sequential spin projection procedure has been carried out. Illustrative calculations for the excited and dissociative states of small molecules have revealed the high quality of the suggested approximate schemes.Original Russian Text Copyright © 2004 by A. V. Luzanov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 771–782, September–October, 2004.     

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions

We present an implementation of the spin‐dependent unitary group approach to calculate spin densities for configuration interaction calculations in a basis of spin symmetry‐adapted functions. Using S² eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. To achieve this, we combine the method to calculate U(n) generator matrix elements developed by Downward and Robb (Theor. Chim. Acta 1977, 46, 129) with the approach of Battle and Gould to calculate U(2n) generator matrix elements (Chem. Phys. Lett. 1993, 201, 284). We also compare and contrast the spin density formulated in terms of the spin‐independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one‐ and two‐electron charge densities.     

Matrix‐covariant representation of high‐order configuration interaction and coupled cluster theories

We present the closed form of the reduced density matrices (RDMs) of arbitrary order for configuration interaction (CI) wave functions at any excitation level, up to the full CI. A special operator technique due to Bogoliubov is applied and extended. It focuses on constructions of matrix‐covariant expressions independent of the basis set used. The corresponding variational CI equations are given in an explicit form containing the matrices related to conventional excitation operators. A subsequent transformation of the latter to an irreducible form makes it possible to generate the matrix‐covariant representation for coupled cluster (CC) models. Here this transformation is performed for a simplified high‐order CC scheme somewhat reminiscent of the quadratic CI model. A generalized spin‐flip approximation closely related to high‐order CI and CC models is presented, stressing on a possible inclusion of nondynamical and dynamical correlation effects for multiple bond breaking. A derivation of the full CI and simple CC models for systems involving effective three‐electron interactions is also given, thereby demonstrating the capability of the proposed method to deal with complicated many‐body problem. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Electronic states of the NiCu molecule determined byab initio Hartree-Fock and configuration interaction methods

The interaction between a Ni atom and a Cu atom in the configurations (3d)⁹(4s)¹ and (3d)¹⁰(4s)¹, respectively, has been calculated usingab initio Hartree-Fock and configuration interaction methods. The chemical bond between the two atoms is due to a bonding 4sσ molecular orbital. Equilibrium distances, dissociation energies and vibrational frequencies are predicted for the low-lying states. Finally the influence of spin-orbit coupling on the low-lying states is considered.