Rajat K. Chaudhuri

The eigenvalue-independent partitioning technique in Fock space: an alternative route to open-shell coupled-cluster theory for incomplete model spaces

Abstract Our recent open-shell coupled-cluster (CC) theory for incomplete model spaces, having valence holes and valence particles, is cast in an alternative form having computational advantages. An eigenvalue-independent partitioning technique in Fock space converts the CC equations for each m -hole, n -particle model space of dimension N (m,n) to a non-Hermitian eigenproblem of larger dimension, whose N (m,n) roots are the energies of interest. This alternative strategy works even in the presence of intruders, as is demonstrated by applying it to the main and satellite peaks of the IP and Auger spectra of HF and to the excitation energies of N 2 .

Aspects of separability in the coupled cluster based direct methods for energy differences

SummaryIn this paper we have discussed in detail the aspects of separability of the energy differences obtained from coupled cluster based “direct” methods such as the open-shell Coupled Cluster (CC) theory and the Coupled Cluster based Linear Response Theory (CC-LRT). It has been emphasized that, unlike the state energiesper se, the energy differences have a semi-local character in that, in the asymptotic limit of non-interacting subsystemsA, B, C, etc., they are separable as ΔEA, ΔEB, ΔEA + ΔEB, etc. depending on the subsystems excited. We classify the direct many-body methods into two categories: core-extensive and core-valence extensive. In the former, we only implicitly subtract the ground state energy computed in a size-extensive manner; the energy differences are not chosen to be valence-extensive (separable) in the semi-local sense. The core-valence extensive theories, on the other hand, are fully extensive — i.e., with respect to both core and valence interactions, and hence display the semi-local separability. Generic structures of the wave-operators for core-extensive and core-valence extensive theories are discussed. CC-LRT is shown to be core-extensive after a transcription to an equivalent wave-operator based form. The emergence of valence disconnected diagrams for two and higher valence problems are indicated. The open-shell CC theory is shown to be core-valence extensive and hence fully connected. For one valence problems, the CC theory and the CC-LRT are shown to be equivalent. The equations for the cluster amplitudes in the Bloch equation are quadratic, admitting of multiple solutions. It is shown that the cluster amplitudes for the main peaks, in principle obtainable as a series inV from the zeroth order roots of the model space, are connected, and hence the energy differences are fully extensive. It is remarkable that the satellite energies obtained from the alternative solutions of the CC equations are not valence-extensive, indicating the necessity of a formal power series structure inV of the cluster amplitudes for the valence-extensivity. The alternative solutions are not obtainable as a power series inV. The CC-LRT is shown to have an effective hamiltonian structure respecting “downward reducibility”. A unitary version of CC-LRT (UCC-LRT) is proposed, which satisfy both upward and downward reducibility. UCC-LRT is shown to lead to the recent propagator theory known as the Algebraic Diagrammatic Construction. It is shown that both the main and the satellite peaks from UCC-LRT for the one valence problems are core-valence extensive owing to the hermitized nature of the underlying operator to be diagonalized.

Applications of multireference perturbation theory to potential energy surfaces by optimal partitioning of H: Intruder states avoidance and convergence enhancement

The minimum basis set hydrogen rectangular system (HRS), consisting of four hydrogen atoms arranged in a rectangle, is examined using a variety of partitionings of the Hamiltonian H for high order single and double reference perturbation computations. The potential energy surface is mapped out over a range of geometries in which the length L of one side of the rectangle is varied. Several criteria are derived governing the necessary conditions for perturbative convergence of two‐state systems, and these criteria are useful in explaining the behavior of the HRS for the range of geometries and partitioning methods investigated. The divergence caused by intruder states, observed by Zarrabian and Paldus [Int. J Quantum Chem. 38, 761 (1990)] for the nondegenerate, double reference space perturbation expansions at L=3.0 a.u. with traditional partitioning methods, is shown to correspond to avoided crossings with negative real values of the perturbation parameter—backdoor intruder states. These intruder state ind...

The improved virtual orbital-complete active space configuration interaction method, a “packageable” efficient ab initio many-body method for describing electronically excited states

We describe a computationally efficient ab initio many-body method that can be used as a “packageable approximation” for computing excited state properties for small to large molecular systems, including those of multiconfigurational character. The method is based on first order multi-reference many-body perturbation theory (MR-MBPT), where the unoccupied valence orbitals are obtained by using an extension of Huzinaga’s improved virtual orbital (IVO) generation technique. Because the method employs a complete active space (CAS) which contains singly, doubly, and higher excited state configurations with respect to the zeroth order ground state configuration, the approach (IVO-CASCI) is capable of providing a more accurate description of the excited states than the widely used packageable configuration interaction with singles (CIS) at a fraction of computational labor. Moreover, unlike the CASSCF approach this IVO-CASCI method does not require iterations and therefore is more computationally efficient and ...

Applications of open-shell coupled cluster theory using an eigenvalue-independent partitioning technique: Approximate inclusion of triples in IP calculations

Abstract Using our eigenvalue-independent partitioning (EIP) approach for the calculation of open-shell coupled cluster (CC) energy differences, we have computed the ionization potentials of HF and H 2 O using basis sets with and without polarization functions. Our results include the three-body cluster operator for the ionized states at the lowest order of approximation. It is found that a CCSD calculation for the ground state, followed by a CCSD calculation for the ionized states - with additional inclusion of triples using the converged CCSD amplitudes - produces results that are accurate up to third order and recovers the relaxation and differential correlation energies consequent on ionization in a balanced and compact manner.

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.

Global three‐dimensional potential energy surfaces of H2S from the ab initio effective valence shell Hamiltonian method

The correlated, size extensive ab initio effective valence shell Hamiltonian (HV) method is used to compute three‐dimensional potential energy surfaces for the ground and several excited electronic states of the H2S molecule. A single calculation of the HV simultaneously generates all states of interest as well as ionization potentials. Particular emphasis is placed on the two lowest 1 1A″ excited surfaces (one valencelike and the other Rydberg‐type) that are involved in recent experiments probing nonadiabatic photodissociation processes. Supplementary effective operator calculations generate three‐dimensional surfaces of dipole moments and transition dipole matrix elements, but emphasis is placed on the transition dipoles relevant to the dissociation process. Comparisons to both experiment and previous calculations for this system support the ability of multireference perturbation methods to describe global potential energy surfaces for open shell systems. We discuss the implication of our calculations f...

Molecular applications of state-specific multireference perturbation theory to HF, H2O, H2S, C2, and N2 molecules

In view of the initial success of the complete active space (CAS) based size-extensive state-specific multireference perturbation theory (SS-MRPT) [J. Phys. Chem. A 103, 1822 (1999)] for relatively diverse yet simple chemically interesting systems, in this paper, we present the computation of the potential energy curves (PEC) of systems with arbitrary complexity and generality such as HF, H(2)O, H(2)S, C(2), and N(2) molecules. The ground states of such systems (and also low-lying singlet excited states of C(2)) possess multireference character making the description of the state difficult with single-reference (SR) methods. In this paper, we have considered the Moller-Plesset (MP) partitioning scheme [SS-MRPT(MP)] method. The accuracy of energies generated via SS-MRPT(MP) method is tested through comparison with other available results. Comparison with FCI has also been provided wherever available. The accuracy of this method is also demonstrated through the calculations of NPE (nonparallelism error) and the computation of the spectroscopic constants of all the above mentioned systems. The quality of the computed spectroscopic constants is established through comparison with the corresponding experimental and FCI results. Our numerical investigations demonstrate that the SS-MRPT(MP) approach provides a balanced treatment of dynamical and non-dynamical correlations across the entire PECs of the systems considered.

Comparison of the perturbative convergence with multireference Möller–Plesset, Epstein–Nesbet, forced degenerate and optimized zeroth order partitionings: The excited BeH2 surface

High order perturbation energies are computed for excited 1A1 states of BeH2 at geometries near the Be→H2 symmetric insertion transition state. The equations of multireference perturbation theory are solved through 30th order to study the difficulties in selecting the appropriate zeroth order Hamiltonian, orbitals, orbital energies, and reference functions for the computations of smooth molecular potential energy surfaces. The origin of the perturbative divergence produced by Moller–Plesset and Epstein–Nesbet partitionings is analyzed using a conceptually simple two-state model constructed using one state each from the reference and orthogonal spaces. The optimized zeroth order partitioning scheme (OPT) for double reference space computations with configurations 1a122a123a12 and 1a122a121b22 produces a truly convergent perturbation expansion through 30th order. The OPT energies are accurate in low orders as compared to the exact (197 dimensional) solution within the basis. The forced valence orbital degen...

Potential energy curve for isomerization of N2H2 and C2H4 using the improved virtual orbital multireference Møller–Plesset perturbation theory

Multireference Møller-Plesset (MRMP) perturbation theory [K. Hirao, Chem. Phys. Lett. 190, 374 (1992)] is modified to use improved virtual orbitals (IVOs) and is applied to study ground state potential energy curves for isomerization and dissociation of the N2H2 and C2H4 molecules. In contrast to traditional MRMP or multistate multiconfiguration quasidegenerate perturbation theory where the reference functions are obtained from (often difficult to converge) state averaged multiconfiguration self-consistent field methods, our reference functions are represented in terms of computationally efficient IVOs. For convenience in comparisons with other methods, a first order complete active space configuration interaction (CASCI) calculation with the IVOs is followed by the use of the IVOs in MRMP to incorporate residual electron correlation effects. The potential energy curves calculated from the IVO-MRMP method are compared with computations using state-of-the-art coupled cluster singles and doubles (CCSD) methods and variants thereof to assess the efficacy of the IVO-MRMP scheme. The present study clearly demonstrates that unlike the CCSD and its variants, the IVO-MRMP approach provides smooth and reliable ground state potential energy curves for isomerization of these systems. Although the rigorously size-extensive completely renormalized CC theory with noniterative triples corrections (CR-CC(2,3)) likewise provides relatively smooth curves, the CR-CC(2,3) calculations overestimate the cis-trans barrier height for N2H2. The ground state spectroscopic constants predicted by the IVO-CASCI method agree well with experiment and with other highly correlated ab initio methods.