Automation of the implementation of spin-adapted open-shell coupled-cluster theories relying on the unitary group formalism

Abstract

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 on the standard molecular (spin) orbital driven algorithms. In this way unnecessary duplications are avoided and efficient codes are developed both for the general formula generation and final executable modules. A thorough testing of this procedure on a number of model cases is described and several illustrative applications at the ab initio level are provided.

Calculation of static molecular properties in the framework of the unitary group based coupled cluster approach

“…Numerous applications carried out so far, and their comparison with the exact full configuration interaction (FCI) results or highly precise data, justify the truncation scheme employed and described above (22,27,31,32). However, it would be worthwhile to explore the role of certain higher order terms in greater detail, particularly for highly stretched geometries.…”

“…To test the capability of our UGA-based CCSD method, as implemented in our codes (27), to provide reliable values of at least low-order static properties for OS systems, we employ the FF approach and examine a few test examples involving states of different multiplicity. These results will also serve us as benchmark values when implementing and testing various versions of the LR approach, which we briefly outline in Sect.…”

“…This software is described in greater detail in ref. 27, and it generates the FORTRAN codes that set up and solve the UGA-CCSD equations and evaluate the corresponding energy. These codes were carefully tested by duplicating the algebraic derivations by hand in the doublet and OS singlet cases, as well as by careful numerical studies (27).…”

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

“…For example, the orthogonally spin-adapted (OSA) [102][103][104][105][106] two-reference SUMRCCSD (SUMRCC singles and doubles) approach [39,41,[45][46][47][48][49][50]54] including all relevant direct and coupling terms [50], which contrary to the statements made in Ref. 107 represents the most complete formulation of this method to date, combined with the open-shell CCSD approach [108], gives 3133 cm −1 for the singlet-triplet separation T 0 . This compares extremely well with the spectroscopically derived value of T 0 of 3147 ± 5 cm −1 [109].…”

State Selective Equation of Motion Coupled Cluster Theory: Some Preliminary Results

“…Schaefer [46] and Li and Paldus [47] we built a tool to aid the derivation and implementation of manybody methodology using automation. The Automatic Program Generator (APG) we developed, generates an efficient Fortran procedure to perform the calculation starting from simple input equations like the ones used in this paper.…”