Yuriy G. Khait

Explication and revision of generalized Van Vleck perturbation theory for molecular electronic structure

A revision of second-order Generalized Van Vleck Perturbation Theory (GVVPT2) for the description of dynamic electron correlation in molecules is presented. It is shown that the basic formulas of the suggested method are well-defined approximations to the theoretically carefully constructed self-consistent quasidegenerate perturbation theory. Furthermore, it is shown that nonlinear responses to the perturbations can be obtained by explicit formulas. The revised GVVPT2 makes active use of the recently introduced concept of macroconfigurations, whereby vast numbers of null Hamiltonian matrix elements are prescreened with minimal computational cost and the remainders are organized for facile computation by Table-CI-like methodology. Moreover, use of macroconfigurations allows the efficient use of incomplete model spaces, which extends drastically the applicability of the method. Representative calculations on model systems studied previously with the original formulation show close agreement and on additional model systems show the wide applicability of the revised formulation.

A self-consistent version of quasidegenerate perturbation theory

A new quasidegenerate perturbation theory is developed that describes the interactions of electronic states of interest with energetically low-lying excited states variationally and with more high-lying excited states perturbatively. The states of interest, the low-lying excited states and the more high-lying excited states, define primary, secondary, and external subspaces, respectively. The task of determination of the lowest solutions of the full configuration interaction (CI) problem is shown to be equivalent to the task of searching iteratively for an optimal primary subspace within the model space spanned by the initial unperturbed primary and secondary states. It is also shown that the present approach, which we refer to as the self-consistent quasidegenerate perturbation theory (SC-QDPT), theoretically satisfies the following criteria: (1) it avoids instabilities due to intruder states; (2) it ensures the additivity of the energy for noninteracting subsystems; (3) the projection of the correlated ...

Configuration-driven unitary group approach for generalized Van Vleck variant multireference perturbation theory.

A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has been improved by 1 or 2 orders of magnitude compared to the previous implementation based on the Table-CI technique. It is shown that the reformulation is applicable to both the second-order (GVVPT2) and third-order (GVVPT3) approximations. Calculations on model problems and on a chemically realistic description of cyclobutadiene are used to illustrate the performance of the method. The calculations on cyclobutadiene, using over 2.3 billion CSFs, provide results on geometric parameters and the barrier height of the automerization reaction in good agreement with established high accuracy results.

Embedding theory for excited states

Using the technique of Perdew and Levy [Phys. Rev. B 31, 6264 (1985)], it is shown that both the density function theory (DFT)-in-DFT and wave function theory (WFT)-in-DFT embedding approaches are formally correct in studying not only the ground state but also a subset of the excited states of the total system. Without further approximations, the DFT-in-DFT embedding approach results in a pair of coupled Euler-Lagrange equations. In contrast to DFT-in-DFT, the WFT-in-DFT approach is shown to ensure a systematic description of excited states if such states are mainly related to excitations within the embedded subsystem. Possible ways for the practical realization of the WFT-in-DFT approach for studying excited states are briefly discussed.

Molecular gradients for the second-order generalized Van Vleck variant of multireference perturbation theory

Recently, a revised second-order generalized Van Vleck perturbation theory (GVVPT2) for the description of molecular electronic structure has been reported [J. Chem. Phys. 117, 4133 (2002)] that is both state selective and of the “perturb-then-diagonalize” type of multireference perturbation theory (MRPT). Herein, formulas for analytic derivatives of the GVVPT2 energy with respect to nuclear perturbations are presented, as are illustrative calculations on model problems. Specifically, it is shown that the modification of the energy denominator, which addresses the so-called intruder-state problem of MRPT, is analytically differentiable with respect to nuclear perturbation and only requires use of matrices available, or directly obtainable, from the underlying multiconfigurational self-consistent field calculation. The developed formalism takes full advantage of the theoretical and computational characteristics of the GVVPT2 energy. In particular, the calculations are performed directly in a spin-adapted b...

A self-consistent quasidegenerate coupled-cluster theory

Abstract A new multireference coupled-cluster theory is suggested which extends the idea of a self-consistent primary space introduced earlier (J. Chem. Phys. 108 (1998) 8317) in the context of quasidegenerate perturbation theory. The suggested approach, which we refer to as the self-consistent quasidegenerate coupled-cluster (SC-QDCC) method, is developed within a Hilbert space framework. The method is both stable to intruder states and reduces to a correct single-reference coupled-cluster theory; moreover, it is appropriate for both strongly and weakly quasidegenerate systems. The theory uses canonical normalization and produces hermitian effective Hamiltonians.

Density Differences in Embedding Theory with External Orbital Orthogonality

First results on electron densities and energies for a number of molecular complexes with different interaction strengths (ranging from ca. 0.3 to 40 kcal/mol), obtained using our recently introduced DFT-in-DFT embedding equations (i.e., Kohn-Sham equations with constrained electron density (KSCED) and external orbital orthogonality (ext orth), KSCED(x, ext orth), where x denotes the single particle support: monomer (m); supermolecular (s); or extended monomer (e)) are compared with densities from supermolecular Kohn-Sham (KS)-DFT calculations and traditional DFT-in-DFT results. Because our methodology does not rely on error-prone potentials that are not present in supermolecular KS-DFT calculations, it allows DFT-in-DFT calculations to achieve much higher accuracy than previous protocols of DFT-in-DFT that employed such potentials. It is shown that whereas conventional DFT-in-DFT embedding theory leads to errors in the electron density at the boundary between subsystems, the situation is remedied when orbital orthogonality between subsystems (i.e., external orthogonality) is enforced. Our approach reproduces KS-DFT total energies at least to the seventh decimal place (and exactly at most geometries) for the tested systems. Potential energy curves (PECs) of the separation of some of the tested systems into fragments are calculated. PECs, obtained with the new equations, using the usual Kohn-Sham equations with constrained electron density and supermolecular basis expansion [KSCED(s, ext orth, v(T) = 0), where v(T) is the nonadditive kinetic potential] were found to be virtually identical to those from conventional KS-DFT; equilibrium distances and interaction energies were reproduced to all reported digits for both local density approximation (LDA) and generalized gradient approximation (GGA) functionals. As an additional approximation, an alternative one-particle space (to the common monomer or supermolecular spaces) in which KS orbitals of a subsystem are expanded is introduced. This expansion, which we refer to as the extended monomer expansion [e.g., KSCED(e)], includes basis functions centered on atom(s) of the complementary subsystem in the interfacial region. Density differences and PECs obtained with the new equations and new one-particle space [i.e., KSCED(e, ext orth, v(T) = 0)] were closely related to those obtained from KSCED(s, ext orth, v(T) = 0). The new approach does not require any supermolecular calculations.

Multireference spin-adapted variant of density functional theory

A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-density functional theory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within density functional theory.

On the Orthogonality of Orbitals in Subsystem Kohn–Sham Density Functional Theory

Abstract A rigorous analysis of the requirements on orbitals of subsystems in the context of Kohn–Sham density functional theory is presented. It is found that conventional constrained electron density formulations, which neglect explicit consideration of orthogonality requirements between subsystems, are exactly correct only in the limit of infinitely separated subsystems. A new method is suggested that takes into account strictly orthogonality constraints and perspectives for its practical implementation are discussed. The performed analysis also provides a practical method for including corrections to conventional methods that approximately compensate for nonorthogonality. It is also shown that the same considerations apply to wave function-in-DFT embedding schemes.

Perturbative triple and quadruple excitation corrections to MRCISD

Abstract A non-iterative approximation to the effects of triple and quadruple excitations in the framework of the multireference configuration interaction method, including single and double excitations (MRCISD), for molecular electronic structure is suggested. The approximation is derived from perturbative expansions of lower and upper bounds of a self-consistent, second-order approximation to the MRCISDTQ energy. Numerical studies on a number of well studied model systems support the hypothesis that the suggested method, which can be referred to as MRCISD(TQ), is a new, viable, ultrahigh accuracy method.