Alternative definition of excitation amplitudes in Multi-Reference state-specific Coupled Cluster

A central difficulty of state-specific Multi-Reference Coupled Cluster (MR-CC) formalisms concerns the definition of the amplitudes of the single and double excitation operators appearing in the exponential wave operator. If the reference space is a complete active space (CAS) the number of these amplitudes is larger than the number of singly and doubly excited determinants on which one may project the eigenequation, and one must impose additional conditions. The present work first defines a state-specific reference-independent operator $\hat{\tilde{T}}^m$ which acting on the CAS component of the wave function $|\Psi_0^m \rangle$ maximizes the overlap between $(1+\hat{\tilde{T}}^m)|\Psi_0^m \rangle$ and the eigenvector of the CAS-SD CI matrix $|\Psi_{\rm CAS-SD}^m \rangle$. This operator may be used to generate approximate coefficients of the Triples and Quadruples, and a dressing of the CAS-SD CI matrix, according to the intermediate Hamiltonian formalism. The process may be iterated to convergence. As a refinement towards a strict Coupled Cluster formalism, one may exploit reference-independent amplitudes provided by $(1+\hat{\tilde{T}}^m)|\Psi_0^m \rangle$ to define a reference-dependent operator $\hat{T}^m$ by fitting the eigenvector of the (dressed) CAS-SD CI matrix. The two variants, which are internally uncontracted, give rather similar results. The new MR-CC version has been tested on the ground state potential energy curves of 6 molecules (up to triple-bond breaking) and a two excited states. The non-parallelism error with respect to the Full-CI curves is of the order of 1 m$E_{\rm h}$.Comment: 11 page

Phase transitions in the Shastry-Sutherland lattice

Two recently developed theoretical approaches are applied to the Shastry-Sutherland lattice, varying the ratio $J'/J$ between the couplings on the square lattice and on the oblique bonds. A self-consistent perturbation, starting from either Ising or plaquette bond singlets, supports the existence of an intermediate phase between the dimer phase and the Ising phase. This existence is confirmed by the results of a renormalized excitonic method. This method, which satisfactorily reproduces the singlet triplet gap in the dimer phase, confirms the existence of a gapped phase in the interval $0.66<J'/J<0.86$Comment: Submited for publication in Phys. Rev.

A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorsky-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double and triple bond breaking. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction (FCI) results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.Comment: 4 figures, 18 page

A renormalized excitonic method in terms of block excitations. Application to spin lattices

Dividing the lattice into blocks with singlet ground state and knowing the exact low energy spectrum of the blocks and of dimers (or trimers) of blocks, it is possible to approach the lowest part of the lattice spectrum through an excitonic type effective model. The potentialities of the method are illustrated on the 1-D frustrated chain and the 1/5-depleted square and the plaquette 2-D lattices. The method correctly locates the phase transitions between gapped and non-gapped phases.Comment: Submitted for publication in Phys. Rev.

Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice

The phase transition occurring in a square 2-D spin lattice governed by an anisotropic Heisenberg Hamiltonian has been studied according to two recently proposed methods. The first one, the Dressed Cluster Method, provides excellent evaluations of the cohesive energy, the discontinuity of its derivative around the critical (isotropic) value of the anisotropy parameter confirms the first-order character of the phase transition. Nevertheless the method introduces two distinct reference functions (either N\'eel or XY) which may in principle force the discontinuity. The Real Space Renormalization Group with Effective Interactions does not reach the same numerical accuracy but it does not introduce a reference function and the phase transition appears qualitatively as due to the existence of two domains, with specific fixed points. The method confirms the dependence of the spin gap on the anisotropy parameter occurring in the Heisenberg-Ising domain

Elementary presentation of self‐consistent intermediate Hamiltonians and proposal of two totally dressed singles and doubles configuration interaction methods

Intermediate Hamiltonians are effective Hamiltonians which are defined on an N‐dimensional model space but which only provide n<N exact eigenvalues and the projections of the corresponding eigenvectors onto the model space. For a single root research, the intermediate Hamiltonian may be obtained from the restriction of the Hamiltonian to the model space by an appropriate, uniquely defined dressing of the diagonal energies or of the first column. Approximate self‐consistent dressings may be proposed. The simplest perturbative form gives the same result as the original 2nd order intermediate Hamiltonian or the ‘‘shifted Bk’’ technique but it is of easier implementation. Self‐consistent inclusion of higher order exclusion principle violating corrections greatly improves the results, especially for nearly degenerate problems, as shown on several illustrative applications. Possible generalizations to enlarged or reduced model spaces are [email protected] ; [email protected]

A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave functio

Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling

Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock one

A self-consistent perturbative evaluation of ground state energies: application to cohesive energies of spin lattices

The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a modified coupled cluster formulation. Applied to a series of spin lattices governed by model Hamiltonians the method leads to simple analytic solutions. The so-calculated cohesive energies are surprisingly accurate. Two examples illustrate its applicability to locate phase transition.Comment: Accepted by Phys. Rev.