Uttam Sinha Mahapatra

A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications

In this paper we present a comprehensive account of a manifestly size-consistent coupled cluster formalism for a specific state, which is based on a reference function composed of determinants spanning a complete active space (CAS). The method treats all the reference determinants on the same footing and is hence expected to provide uniform description over a wide range of molecular geometry. The combining coefficients are determined by diagonalizing an effective operator in the CAS and are thus completely flexible, not constrained to preassigned values. A separate exponential-type excitation operator is invoked to induce excitations to all the virtual functions from each reference determinant. The linear dependence inherent in this choice of cluster operators is eliminated by invoking suitable sufficiency conditions, which in a transparent manner leads to manifest size extensivity. The use of a CAS also guarantees size consistency. We also discuss the relation of our method with the extant state-specific...

Molecular Applications of a Size-Consistent State-Specific Multireference Perturbation Theory with Relaxed Model-Space Coefficients.

We explore in this paper the efficacy of the Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) perturbative counterparts of our recently developed multireference state-specific coupled-cluster formalism (SS-MRCC) with a complete active space (CAS). It is size-extensive and is designed to avoid intruders. The parent SS-MRCC method uses a sum-of-exponentials type of Ansatz for the wave operator. The redundancy inherent in such a choice is resolved by postulating suitable sufficiency conditions which at the same time ensure size-extensivity and size-consistency. The combining coefficients c μ for φμs are completely relaxed and are obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of our interest. By invokation of a suitable partitioning of the Hamiltonian, very convenient perturbative versions of the formalism in both the RS and the BW forms are developed for the second-order energy. The unperturbed Hamiltonian is akin to the Epstein-Nesbet type when at least one of the orbitals is inactive and is the entire active portion of the Hamiltonian when all the orbitals involved are active. Illustrative numerical applications are presented for potential energy surfaces (PES) of a number of model and realistic systems where intruders exist and for molecules in their ground states with pronounced multireference character. Single reference MBPT and effective Hamiltonian-based multireference MBPT second-order results are also presented for comparisons. The results indicate the smooth performance of our state-specific perturbative formalisms in and around the region of intruders in the PES, indicating their suitability in bypassing intruders. In contrast, the effective Hamiltonian-based MBPT methods behave poorly in the regions of intruders.

A state-specific approach to multireference coupled electron-pair approximation like methods: Development and applications

The traditional multireference (MR) coupled-cluster (CC) methods based on the effective Hamiltonian are often beset by the problem of intruder states, and are not suitable for studying potential energy surface (PES) involving real or avoided curve crossing. State-specific MR-based approaches obviate this limitation. The state-specific MRCC (SS-MRCC) method developed some years ago can handle quasidegeneracy of varying degrees over a wide range of PES, including regions of real or avoided curve-crossing. Motivated by its success, we have suggested and explored in this paper a suite of physically motivated coupled electron-pair approximations (SS-MRCEPA) like methods, which are designed to capture the essential strength of the parent SS-MRCC method without significant sacrificing its accuracy. These SS-MRCEPA theories, like their CC counterparts, are based on complete active space, treat all the reference functions on the same footing and provide a description of potentially uniform precision of PES of states with varying MR character. The combining coefficients of the reference functions are self-consistently determined along with the cluster amplitudes themselves. The newly developed SS-MRCEPA methods are size-extensive, and are also size-consistent with localized orbitals. Among the various versions, there are two which are invariant with respect to the restricted rotations among doubly occupied and active orbitals separately. Similarity of performance of this latter and the noninvariant versions at the crossing points of the degenerate orbitals imply that the all the methods presented are rather robust with respect to the rotations among degenerate orbitals. Illustrative numerical applications are presented for PES of the ground state of a number of difficult test cases such as the model H4, H(8) problems, the insertion of Be into H(2), and Li(2), where intruders exist and for a state of a molecule such as CH(2), with pronounced MR character. Results obtained with SS-MRCEPA methods are found to be comparable in accuracy to the parent SS-MRCC and FCI/large scale CI results throughout the PES, which indicates the efficacy of our SS-MRCEPA methods over a wide range of geometries, despite their neglect of a host of complicated nonlinear terms, even when the traditional MR-based methods based on effective Hamiltonians fail due to intruders.

Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients

Abstract We explore the Rayleigh–Schrodinger and the Brillouin–Wigner perturbative counterparts of our recently developed state-specific coupled-cluster formalism with a complete active space. It is size-extensive and designed to avoid intruders. For each reference determinant φ μ , there is a separate cluster operator T μ . The redundancy inherent in such a choice is resolved by postulating suitable sufficiency conditions which at the same time ensure size-extensivity and size-consistency. The combining coefficients c μ for φ μ s are completely relaxed and obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of the state. We illustrate size-consistency of the perturbative formalisms with an example model problem.

Development of a linear response theory based on a state-specific multireference coupled cluster formalism

We present in this paper a linear response theory based on our recently developed state-specific multireference coupled cluster (SS-MRCC) method to compute excited state energies for systems whose ground state has a pronounced multireference character. The SS-MRCC method is built on complete active space reference functions, and is designed to treat quasidegeneracy of varying degrees while bypassing the intruder problem. The linear response theory based on such a function [multireference coupled cluster based linear response theory (MR-CCLRT)] offers a very convenient access to computation of excited states and, in particular, to generation of potential energy surfaces (PES) for excited states where a traditional response formulation based on a single reference theory will fail due to the quasidegeneracy at some regions of the PES and the effective Hamiltonian-based multireference response methods would be plagued by intruders. An attractive feature of the MR-CCLRT is that the computed excitation energies...

State-specific multi-reference coupled electron-pair approximation like methods : formulation and molecular applications

We present two variants of state-specific multi-reference coupled electron-pair type approximants (SS-MRCEPA) of our recently formulated state-specific multi-reference coupled-cluster (SS-MRCC) theory. Just like the parent SS-MRCC theory, these are formulated with a complete active space, and are rigorously size-extensive and size-consistent. They also bypass the intruder problem very efficiently. The efficacy of the methods is illustrated with the computation of the ground state potential energy surface of the trapezoidal H4 model, where the ground state requires a two-determinantal model space and the effective hamiltonian methods face intruders.

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.

Property calculations using perturbed orbitals via state-specific multireference coupled-cluster and perturbation theories

In this paper we apply the recently developed state-specific multireference coupled-cluster and perturbation theories to calculate electrical properties such as dipole moment and static polarizability using perturbed orbitals in finite fields. The theories are built on complete active space reference functions, and are designed to treat quasidegeneracy of varying degrees while bypassing the intruder problem. Numerical results are presented for the model systems H4 with trapezoidal geometry and the lowest two singlet states of CH2. Both the systems require a multireference formulation due to quasidegeneracy. In the field-free situation, the former encounters intruders at an intermediate trapezoidal geometry in the traditional treatment using effective Hamiltonians, while the latter shows a pronounced multireference character in the two singlet states. This affects the response properties in the presence of a perturbing field. A comparison with the full CI results in the same basis indicates the efficacy of...

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.

Application of state-specific multireference Møller–Plesset perturbation theory to nonsinglet states

We present molecular applications of a spin free size-extensive state-specific multireference perturbation theory (SS-MRPT), which is valid for model functions of arbitrary spin and generality. In addition to the singlet states, this method is equally capable to handle nonsinglet states. The formulation based on Rayleigh-Schrodinger approach works with a complete active space and treats each of the model space functions democratically. The method is capable of handling varying degrees of quasidegeneracy and of ensuring size consistency as a consequence of size extensivity. In this paper, we illustrate the effectiveness of the Møller-Plesset (MP) partitioning based spin free SS-MRPT [termed as SS-MRPT(MP)] in computations of energetics of the nonsinglet states of several chemically interesting and demanding molecular examples such as LiH, NH(2), and CH(3). The spectroscopic constants of (3)Sigma(-) state of NH and OH(+) molecular systems and the ground (1)Sigma(g) (+) as well as excited (3)Sigma(u)(+) states of N(2) have been investigated and comparison with experimental and full configuration interaction values (wherever available) has also been provided. We have been able to demonstrate here that the SS-MRPT(MP) method is an intrinsically consistent and promising approach to compute reliable energies of nonsinglet states over different geometries.