Barnali Datta

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.

The construction of a size-extensive intermediate Hamiltonian in a coupled-cluster framework

Abstract A size-extensive formulation for an intermediate Hamiltonian H int , furnishing size-extensive energies for the main roots, is presented. The working model space, comprised of the main and intermediate space, is taken as complete. The starting point is a shifted Bloch equation derived by us, involving shift operators generated by the projector spanned by the intermediate eigenvectors of H int . It is shown that a manifestly size-extensive H int can be constructed in the coupled-cluster framework provided we choose the shift operator explicitly as additively separable and the associated intermediate wave operator R as multiplicatively separable.

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.

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.

Method of intermediate hamiltonians via eigenvalue-independent partitioning: application to theoretical spectroscopy

Abstract We develop and apply in this paper a coupled cluster (CC)-based intermediate hamiltonian method that is suitable for describing both the lower- and higher-lying excited/ionized states relative to a closed-shell ground state. Generation of the main roots corresponding to the lower-lying states is attempted via an open-shell CC expansion. This expansion dresses the hamiltonian appropriately to incorporate the effect of the virtual space Q in a size-extensive manner. We have shown that by recasting the CC equations in a pseudo-eigenvalue equation form, we may also generate the higher-lying states approximately. The space in which the dressed matrix works is the union of the starting model space (which now becomes the “main” model space, P m ) and the space reached by the action of the first power of the cluster operator on the main model space functions (they span the intermediate space P i ). Using the wave operator in the Fock space, the same kind of dressing is maintained for both the main and the intermediate functions via the use of the same transformed hamiltonian for both these types. This dressing thus incorporates the same decoupling of the Q space from both the P m and P i spaces. The P i , roots, however, miss the “extra” dressing which should arise because of extra hole-particle vacancies in the P i -space functions; to this extent, they are distorted. The pseudo-eigenvalue form of our working equations bypasses the difficult problem of intruder states in a straightforward and obvious way. Applications to compute the main and satellite Auger spectra of H 2 O produce encouraging results, indicating the viability of the method.

Treatment of quasi-degeneracy in single-reference coupled-cluster theory. Separation of dynamical and nondynamical correlation effects

Abstract We show that the most important nondynamical correlation effects of quasidegeneracy arising, for example, out of bond-breaking, can be effectively handled using low-body cluster operators (usually up to rank two) via a modification of single-reference coupled-cluster (CC) theory. This is done by separating the effects of cluster operators leading to dynamical and nondynamical correlations. The former leads to direct excitations to the virtual functions χ i from the reference function /gf, and the latter excites to χ i via intermediates / gf μ quasi-degenerate with /gf. By utilizing a separability condition for the dynamical and nondynamical correlation energies, a rigorously size-extensive and size-consistent CC theory is developed which should be well-behaved and accurate at bond-breaking geometries.

A spin-adapted coupled-cluster based linear response theory for double ionization potentials

We developed in this article a spin-adapted formulation of the coupled-cluster based linear response theory (CC-LRT) for computing double-ionization potentials (DIPs), which may be experimentally observed by Auger spectroscopy. CC-LRT is a multireference generalization of the CC theory where the energy differences have no disconnected vacuum (core) diagrams, signifying core-extensivity. For the spin-adaptation of the CC-LRT equations for the singlet and triplet manifolds, we used the Young-Yamanouchi orthogonal spin-eigenfunctions. The orbital version of the CC-LRT equations are then automatically generated by the conjugate projection operators of Young-Yamanouchi spin functions. We illustrated the working of our spin-adaptation procedure by confining our CC-LRT equations to the space of 2h and 1p–3h ionized determinants. As numerical application of our formalism, we computed the Auger kinetic energies of HF and H2O. We also analyzed the nature of size-extensivity of the DIPs generated by CC-LRT and showed explicitly that when the molecule is composed of two noninteracting fragments the computed DIPs are either DIPs of fragment A or B or a composite DIP depending on both A and B, which are just not sum of ionization potentials (IPs) of A and B. This analysis is done to underscore the fact that DIPs from CC-LRT is only core-extensive and not fully extensive.