Xiangzhu Li

Reduced multireference CCSD method: An effective approach to quasidegenerate states

Standard multireference (MR) coupled cluster (CC) approaches are based on the effective Hamiltonian formalism and generalized Bloch equation. Their implementation, relying on the valence universal or state universal cluster Ansatz, is very demanding and their practical exploitation is often plagued with intruder state and multiple solution problems. These problems are avoided in the so-called state selective or state specific (SS) MR approaches that concentrate on one state at a time. To preserve as much as possible the flexibility and generality offered by the general MR CC approaches, yet obtaining a reliable and manageable algorithm, we propose a novel SS strategy providing a size-extensive CC formalism, while exploiting the MR model space and the corresponding excited state manifold. This strategy involves three steps: (i) The construction of a variational configuration interaction (CI) wave function within the singly (S) and doubly (D) excited state manifold, (ii) the cluster analysis of this CI wave...

Reduced multireference couple cluster method. II. Application to potential energy surfaces of HF, F2, and H2O

The so-called reduced multireference (RMR) coupled cluster method restricted to singly and doubly excited clusters (CCSD) [see X. Li and J. Paldus, J. Chem. Phys. 107, 6257 (1997)] is employed to compute potential energy surfaces for the HF, F2 and H2O molecules over a wide range of geometries using basis sets of a double zeta (DZ) and DZ plus polarization (DZP) quality. The RMR-CCSD method belongs to a class of externally corrected CCSD approaches, which rely on a suitable non-CC wave function that is flexible enough to describe the dissociation process at hand and is used as a source of 3- and 4-body cluster amplitudes. These amplitudes are in turn used to achieve a more appropriate decoupling of the full CC chain of equations than that leading to the standard CCSD equations. The RMR-CCSD method employs for this purpose a MR-CISD wave function obtained with a relatively small active or model space. To illustrate the capabilities of this approach, the computed potential energy curves for the HF, F2 and H...

AUTOMATION OF THE IMPLEMENTATION OF SPIN-ADAPTED OPEN-SHELL COUPLED-CLUSTER THEORIES RELYING ON THE UNITARY GROUP FORMALISM

A new implementation of the orthogonally spin‐adapted open‐shell (OS) coupled‐cluster (CC) formalism that is based on the unitary group approach to many‐electron correlation problem is described. Although the emphasis is on the so‐called state specific single‐reference but multiconfigurational OS CC approach, the developed algorithms as well as the actual codes are also amenable to multireference CC applications of the state‐universal type. A special attention is given to simple OS doublets and OS singlet and triplet cases, the former being applicable to the ground states of radicals and the latter to the excited states of closed shell systems. The encoding of the underlying formalism is fully automated and is based on a convenient decomposition of the Hamiltonian into the effective zero‐, one‐, and two‐orbital contributions as well as on the general strategy that focuses on the excitation operator driven evaluation of individual absolute, linear, quadratic, etc., coupled cluster coefficients, rather than...

General-model-space state-universal coupled-cluster theory: Connectivity conditions and explicit equations

We present a new version of the state-universal (SU), multireference, coupled-cluster (CC) theory that is capable of handling completely general, incomplete model spaces. This is achieved by exploiting the concept of “locality” for the active molecular spin orbitals and by introducing the constraining conditions (C conditions) on cluster amplitudes that are associated with the internal excitations transforming one reference configuration into another one. These C conditions make it possible to represent the exact (i.e., full configuration interaction) wave function via the SU CC cluster ansatz based on an arbitrary model space. The C conditions are then taken into account together with the standard SU CC equations for the external amplitudes, thus enabling us to reach the exact result in the limit, while preserving the connectivity property and thus the size extensivity. We also present compact expressions for the matrix elements of the effective Hamiltonian as well as the explicit expressions for the mos...

Simultaneous handling of dynamical and nondynamical correlation via reduced multireference coupled cluster method: Geometry and harmonic force field of ozone

The geometry and vibrational frequencies of the ozone molecule are studied using the reduced multireference coupled cluster method with singles and doubles (RMR CCSD) relying on a two-electron/two-orbital (2,2) active space. The role played by the choice of the reference space is analyzed in detail by considering both the spin adapted, two-configuration reference space and the complete three-configuration reference space based on the (2,2) active space. It is shown that while the two-reference RMR CCSD approach, using the C2v symmetry-adapted (2,2) active space, provides a better description of the geometry and harmonic frequencies of symmetric vibrational modes than the standard single-reference (SR) CCSD method, the three-reference approach is essential to achieve an accurate description of the harmonic frequency of the asymmetric stretching mode. A unique behavior of ozone in this regard is highlighted by a comparison with other symmetric triatomics. The comparison with results obtained by other method...

Reduced multireference coupled cluster method: Ro-vibrational spectra of N2

The reduced multireference (RMR) coupled cluster method with singles and doubles (CCSD), relying on four- and eight-dimensional reference spaces, is employed to generate the potential energy curve for the nitrogen molecule, using both the correlation-consistent polarized valence-triple-zeta (cc-pVTZ) and atomic natural orbital basis sets. The resulting potentials are then used to compute the ro-vibrational term values, which are compared with the available experimentally determined values. Moreover, a direct comparison with the measured spectral line frequencies, for both the fundamental rotational Raman band and the vibrationally excited Q branches, is also carried out. Comparisons with the single reference CCSD, as well as with the corresponding multireference configuration interaction results that serve as the external source for RMR CCSD, are also made. An excellent performance of RMR CCSD, and its systematic improvement with the increasing dimension of the reference space employed, is demonstrated fo...

DISSOCIATION OF N2 TRIPLE BOND : A REDUCED MULTIREFERENCE CCSD STUDY

Abstract The reduced multireference (RMR) coupled cluster method with singles and doubles is applied to the dissociation of the ground state of the nitrogen molecule. It is shown that even with a relatively modest highly truncated reference space one obtains an accurate potential over a wide range of internuclear separations.

The general-model-space state-universal coupled-cluster method exemplified by the LiH molecule

The salient features of the recently introduced general-model-space (GMS) state-universal (SU) coupled-cluster (CC) method are illustrated on the case of the LiH molecule. Describing the breaking of the Li–H bond by relying on an open-shell-type GMS reveals the importance of the connectivity conditions (C conditions), which represent a crucial new ingredient of the GMS SU CC theory. Only when we properly account for these C conditions can we uniquely represent the full configuration interaction (FCI) wave functions in terms of the multireference SU exponential cluster ansatz and recover the FCI energies via the GMS SU CC method, assuming that all the relevant clusters at a given level of the theory are considered. Drawing on various GMSs, we compute the potential energy curves for three 1Σ+, two 3Σ+, three 1Π, and three 3Π states, using the GMS SU CC method truncated at the singly- and doubly-excited level (GMS SU CCSD), as well as the externally corrected (N,M)-CCSD method that exploits the NR-CISD wave ...

Externally corrected singles and doubles coupled cluster methods for open-shell systems

The idea of an externally corrected singles and doubles coupled cluster (CCSD) method using an independent source for connected triples and quadruples is generalized to open-shell high-spin states and implemented within the framework of the unitary group based CCSD method. New and more efficient programs are designed to perform cluster analysis of ab initio wave functions and to calculate corrections to standard CCSD equations. The method is applied to describe a single bond breaking of OH in the 2Π state, using both double zeta (DZ) and DZ plus polarization (DZP) basis sets. Both full or limited configuration interaction (CI) within small and carefully chosen active spaces (AS) and complete AS self-consistent-field (CASSCF) wave functions are employed as external sources for triple and quadruple corrections. It is shown that the CI or CASSCF corrected CCSD method can effectively account for higher than pair clusters while requiring only a small additional computational effort over that of the standard CC...

Electronic structure of organic diradicals: Evaluation of the performance of coupled-cluster methods

The performance of (i) the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR CCSD) that employs a modest-size MR CISD wave function as an external source for the most important (primary) triples and quadruples in order to account for the nondynamic correlation effects in the presence of quasidegeneracy, (ii) the RMR CCSD(T) method that adds a perturbative correction for the remaining (secondary) triples to the RMR CCSD energy, and (iii) the recently developed partially linearized MR CCSD method, which determines primary triples and quadruples using a subset of linear CC equations projected onto the corresponding higher-than-doubly excited configurations, are tested by considering the singlet-triplet splitting for several diradicals, ranging from a prototypical methylene radical to trimethylenemethane, and benzyne and pyridynium cation isomers. Both RHF and multiconfigurational self-consistent field molecular orbitals are employed. The equilibrium geometries for the lowest-lying singlet and triplet states are determined using both the density functional theory (DFT) and various CC approaches, and a comparison with both the experiment and other theoretical results, wherever available, is made. The RMR CCSD(T) results provide the most satisfactory description in all cases. The dependence of the MR diradical character on a spatial separation of radical centers, as well as the artifactual DFT geometry in the case of benzyne and pyridynium meta-isomers, is also pointed out.