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The spin-free analogue of Mukherjee's state-specific multireference coupled cluster theory

### Abstract

In this paper, we develop a rigorously spin-adapted version of Mukherjee's state-specific multireference coupled clustertheory (SS-MRCC, also known as Mk-MRCC) [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. **110**, 6171 (1999)] for reference spaces comprising open-shell configurations. The principal features of our approach are as follows: (1) The wave operator Ω is written as Ω = ∑_{μ}Ω_{μ}|ϕ_{μ}〉*c* _{μ}, where {ϕ_{μ}} is the set of configuration state functions spanning a complete active space. (2) In contrast to the Jeziorski–Monkhorst Ansatz in spin-orbital basis, we write Ω_{μ} as a power series expansion of cluster operators *R* ^{μ} defined in terms of spin-free unitary generators. (3) The operators *R* ^{μ} are either closed-shell-like n hole-n particle excitations (denoted as *T* ^{μ}) or they involve valence (active) destruction operators (denoted as *S* ^{μ}); these latter type of operators can have active–active scatterings, which can also carry the same active orbital labels (such *S* ^{μ}’s are called to have spectator excitations). (4) To simulate multiple excitations involving powers of cluster operators, we allow the *S* ^{μ}’s carrying the same active orbital labels to contract among themselves. (5) We exclude *S* ^{μ}’s with direct spectator scatterings. (6) Most crucially, the factors associated with contracted composites are chosen as the inverse of the number of ways the *S* ^{μ}’s can be joined among one another leading to the same excitation. The factors introduced in (6) have been called the automorphic factors by us. One principal thrust of this paper is to show that the use of the automorphic factors imparts a remarkable simplicity to the final amplitude equations: the equations consist of terms that are at most quartic in cluster amplitudes, barring only a few. In close analogy to the Mk-MRCC theory, the inherent linear dependence of the cluster amplitudes leading to redundancy is resolved by invoking sufficiency conditions, which are exact spin-free analogues of the spin-orbital based Mk-MRCC theory. This leads to manifest size-extensivity and an intruder-free formulation. Our formalism provides a relaxed description of the nondynamical correlation in presence of dynamical correlation. Pilot numerical applications to doublet systems, e.g., potential energy surfaces for the first two excited ^{2} *A*' states of asymmetric H_{2}S^{+} ion and the ground ^{2}Σ^{+}state of BeH radical are presented to assess the viability of our formalism over an wide range of nuclear geometries and the manifest avoidance of intruder state problem.

© 2011 American Institute of Physics

Received Wed Oct 27 00:00:00 UTC 2010
Accepted Mon Dec 20 00:00:00 UTC 2010
Published online Mon Feb 07 00:00:00 UTC 2011

Acknowledgments:
The authors are grateful to Professor Josef Paldus for pointing out the doublet instability of ROHF wave function for BeH and for Refs. 43 and 44. We also thank Professor Marcel Nooijen for his constructive criticisms. D.M. acknowledges DST, India for the J. C. Bose National Fellowship, the Indo-EU MONAMI Fellowship, theIndo-EU Bilateral Grant, and also the Indo-Swedish Bilateral Project.

Article outline:

I. INTRODUCTION
II. Mk-MRCC THEORY USING JM ANSATZ
III. THE SPIN-FREE ANALOGUE OF THE JEZIORSKI–MONKHORST ANSATZ
A. General preliminaries
B. Structure of the cluster expansion Ansatz for noncommuting operators: A perturbative analysis
C. The MR-COSCC Ansatz: Features and advantages
IV. DEVELOPMENT OF SPIN-ADAPTED SS MRCC THEORY USING THE MR-COSCC ANSATZ
V. SPECIFIC FEATURES OF THE SPIN-ADAPTED SS-COS-MRCC FORMALISM
A. Avoidance of intruders
B. Connectedness of the amplitude equations
VI. RESULTS AND DISCUSSIONS
A. An outline of the SS-COS-MRCC algorithm
B. Pilot numerical applications
1. Potential energy surfaces for the first two excited ^{2} *A*' states of asymmetric H_{2}S^{+} ion
2. Potential energy surface for the ground ^{2}Σ^{+} state of BeH radical
VII. SUMMARY AND FUTURE OUTLOOK

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