A sequential transformation approach to the internally contracted multireference coupled cluster method

Abstract

The internally contracted multireference coupled cluster (ic-MRCC) approach is formulated using a new wave function ansatz based on a sequential transformation of the reference function (sqic-MRCC). This alternative wave function simplifies the formulation of computationally viable methods while preserving the accuracy of the ic-MRCC approach. The structure of the sqic-MRCC wave function allows folding the effect of the single excitations into a similarity-transformed Hamiltonian whose particle rank is equal to the one of the Hamiltonian. Consequently, we formulate an approximation to the sqic-MRCC method with singles and doubles (included respectively up to fourfold and twofold commutators, sqic-MRCCSD[2]) that contains all terms present in the corresponding single-reference coupled cluster scheme. Computations of the potential energy curves for the dissociation of BeH(2) show that the untruncated sqic-MRCCSD scheme yields results that are almost indistinguishable from the ordinary ic-MRCCSD method. The energy obtained from the computationally less expensive sqic-MRCCSD[2] approximation is found to deviate from the full ic-MRCCSD method by less than 0.2 mE(h) for BeH(2), while, in the case of water, the harmonic vibrational frequencies of ozone, the singlet-triplet splitting of p-benzyne, and the dissociation curve of N(2), sqic-MRCCSD[2] faithfully reproduces the results obtained via the ic-MRCCSD scheme truncated to two commutators. A formal proof is given of the equivalence of the ic-MRCC and sqic-MRCC methods with the internally contracted and full configuration interaction approaches.

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

“…8 IC, now widely used in MR theories 7,9,41,[51][52][53] aggressively truncates the many body basis and reduces the cost of the calculation from exponential to merely polynomial in the number of active space orbitals. The difficulty with IC is that the working equations become extremely cumbersome and can often only be derived using domain specific computer algebra systems.…”

“…Methods of this class are hierarchies based on truncated multireference configuration interaction (MRCI) 10,35,36 , various flavors of perturbation theory 6,37-39 and coupled cluster theory. 40,41 However, the established methods of these classes are based on CI treatments of the static correlation, which either makes them cumbersome to apply (RAS, GAS) [42][43][44] , or limits them to small active spaces (CAS). Some alternative approaches fall outside this static-dynamic partitioning framework (e.g., methods based on geminals 45,46 , Jastrow factors 47 or reduced density matrices 48 ); while promising, they have so far not matured into routinely applied methods.…”

A Lagrange multiplier approach for excited state properties through intermediate Hamiltonian formulation of Fock space multireference coupled-cluster theory

“…10,11 However, in cases of molecular bond dissociation and open shell states, a multi-reference zeroth order description becomes essential for the treatment of non-dynamic electron correlation and dynamic correlation is taken care of by the built in exponential feature of wave operator. These methods are collectively referred to as multi-reference coupled cluster (MRCC) [12][13][14][15][16][17][18][19][20] methods. Existing MRCC approaches can be divided into three basic categories: Fock space (FS) 12,13 or valance universal (VU), Hilbert space (HS) 14 or state universal (SU), and state selective (SS) [15][16][17][18][19][20] CC.…”

“…These methods are collectively referred to as multi-reference coupled cluster (MRCC) [12][13][14][15][16][17][18][19][20] methods. Existing MRCC approaches can be divided into three basic categories: Fock space (FS) 12,13 or valance universal (VU), Hilbert space (HS) 14 or state universal (SU), and state selective (SS) [15][16][17][18][19][20] CC. The first two approaches are commonly in the class of multi-root MRCC methods, as they are built on the concept of Bloch equation based effective Hamiltonian 21,22 acting within a model space.…”

“…Intruder state problem can also be avoided by using SSMRCC methods. Among few variants of SSMRCC method in literature are Brillouin-Wigner (BW) MRCC 15,16 ansatz, exponential MR wave function ansatz (MRexpT), 17 the state-specific MRCC method suggested by Mukherjee and co-workers (Mk-MRCC), 18 and internally contracted MRCC (ic-MRCC) 19 theory. Recently, Nooijen and co-workers proposed multi-reference EOMCC (MR-EOMCC) 20 The IH formulation of FSMRCC, which leads to a completely new method, has been developed and extensively applied by Kaldor and co-workers.…”