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In this paper, we develop a rigorously spin-adapted version of Mukherjee's state-specific multireference coupled cluster theory (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 = ∑μΩμ|[lowercase_phi_synonym]μ>cμ, where {[lowercase_phi_synonym]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 Ωμ as a power series expansion of cluster operators Rμ defined in terms of spin-free unitary generators. (3) The operators Rμ are either closed-shell-like n hole-n particle excitations (denoted as Tμ) or they involve valence (active) destruction operators (denoted as Sμ); these latter type of operators can have active-active scatterings, which can also carry the same active orbital labels (such Sμ's are called to have spectator excitations). (4) To simulate multiple excitations involving powers of cluster operators, we allow the Sμ's carrying the same active orbital labels to contract among themselves. (5) We exclude Sμ'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 Sμ'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 2A' states of asymmetric H2S+ ion and the ground 2Σ+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. [ABSTRACT FROM AUTHOR]

The parent state-specific multireference coupled-cluster (SS-MRCC) theory proposed by Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)], though rigorously size-extensive and also size-consistent with localized orbitals, has some deficiencies in the minimal truncation scheme, viz. at the singles and doubles (SD) level (SS-MRCCSD). SS-MRCCSD does not involve the direct coupling of all the model functions with a given virtual function belonging to the uncontracted multiconfiguration CISD space. It also does not involve, even in the linear power of a cluster operator Tμ, the direct coupling of the virtual functions χlμ, which are up to doubly excited with respect to a model function φμ to the other virtual functions of the MRCISD space which can be generated by triple and quadruple excitations from φμ. We argue that inclusion of a selection of triples and quadruples involving at most two inactive orbital excitations from every φμ would ameliorate the shortcoming of the incomplete coupling of the triply and quadruply excited virtual functions which can couple with the singly and doubly excited ones. This extended ansatz for our SS-MRCC theory, to be called SS-MRCCSDtq by us, would still miss the direct coupling of the manifold of the model functions {φλ,λ≠μ} to singly and doubly excited virtual functions. However, this effect is expected to be less significant than the lack of the more complete virtual space couplings, these functions being many more numerous, suggesting the new methods to be significantly improved schemes. Excellent results on the potential energy surfaces of small molecules involving single, double, and triple bond dissociation bear out our expectations fully. [ABSTRACT FROM AUTHOR]

The state-specific multireference coupled-cluster (SS-MRCC) ansatz developed by Mukherjee and co-workers [J. Chem. Phys. 110, 6171 (1999)] has been implemented by means of string-based techniques. The implementation is general and allows for using arbitrary complete active spaces of any spin multiplicity and arbitrarily high excitations in the cluster operators. Several test calculations have been performed for single- and multiple-bond dissociations of molecular systems. Our experience shows that convergence problems are encountered when solving the working equations of the SS-MRCC in the case the weight of one or more reference functions tends to take on very small values. This is system specific and cannot yet be handled in a black-box fashion. The problem can be obviated by either dropping all the cluster amplitudes from the corresponding model functions with coefficients below a threshold or by a regularization procedure suggested by Tikhonov or a combination of both. In the current formulation the SS-MRCC is not invariant with respect to transformation of active orbitals among themselves. This feature has been extensively explored to test the degree of accuracy of the computed energies with both pseudocanonical and localized active orbitals. The performance of the method is assessed by comparing the results with the corresponding full configuration interaction (CI) values with the same set of orbitals (correlated and frozen). Relative efficacies of CI methods such as MRCI singles and doubles with the same active space and size-extensivity corrected ones such as MR averaged coupled pair functional and MR averaged quadratic CC have also been studied. Allied full-fledged CC methods have also been employed to see their relative performance vis-à-vis the SS-MRCC. These latter methods are the complete-active-space-inspired single-reference (SR) CC based SS theory and the single-root MR Brillouin–Wigner CC. Our benchmark results indicate that the performance of the SS-MRCC is generally quite good for localized active orbitals. The performance with the pseudocanonical orbitals, however, is sometimes not as satisfactory as for the localized orbitals. [ABSTRACT FROM AUTHOR]

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two-electron Gaunt term, not usually taken into consideration, has been estimated at the Self-Consistent Field (ΔSCF) level and is found to become increasingly important and eventually quite prominent for molecules with third period atoms and below. The accuracies of the IPs computed using UGA-OSCC are found to be of the same order as the Coupled Cluster Singles Doubles (ΔCCSD) values while being free from spin contamination. Since the UGA-OSCC uses a common set of orbitals for the ground state and the ion, it obviates the need of two N5 AO to MO transformation in contrast to the ΔCCSD method. [ABSTRACT FROM AUTHOR]

The k-particle reduced density matrices γk for a singlet state or a spin-orientation averaged ensemble are invariant under the spin rotation group SU(2), i.e. they are independent of spin, even if they are expressed in terms of spin orbitals. The γk contain the same information as their spinfree counterparts Γk expressed in terms of spinfree orbitals. However, the relation between the two quantities is, by no means, elementary. The summation over spin is particularly demanding and surprisingly complicated for the k-particle density cumulants λk and for the formulation of a generalised normal ordering with respect to an arbitrary reference state, including the generalised Wick theorem. Plausible extrapolations from small k turned out to be unjustified and some published expressions for k = 4 need to be revised. A compact general result, valid for all k has not yet been found. [ABSTRACT FROM AUTHOR]