Multireference coupled-cluster response approach for the calculation of static properties

Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+T^*(3). We present two approximate fourth-order schemes, MRCCSD+T^*−a(4) and MRCCSD+T^*(4). The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype Li₂ molecule, using four different basis sets, as well as BeO and CH⁺. We have calculated the vertical electron affinities of Li₂ at the geometry of the neutral Li₂ molecule. We also present the vertical ionization potentials of the Li₂ anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH⁺, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

Fock-Space Coupled Cluster Theory: Systematic Study of Partial Fourth Order Triples Schemes for Ionization Potential and Comparison with Bondonic Formalism

In this paper, we have made a systematic study of partial fourth order perturbative schemes due to triples to compute the ionization potential within Fock-space multi-reference coupled-cluster theory. In particular, we have obtained computationally less expensive correlation schemes due to fourth order triples. Prototype examples have been considered to explore the efficacy of the approximate methods mentioned, while the bondonic formalism supporting the bonding phenomenology is also respectively for the first time here advanced.

Effect of Triples to Dipole Moments in Fock-Space Multireference Coupled Cluster Method

In this paper, we present the new implementation of partial triples for the dipole moment of doublet radicals in Lagrangian formulation of Fock-space multireference coupled cluster (Λ-FSMRCC) response method. We have implemented a specific scheme of noniterative triples, in addition to singles and doubles schemes, which accounts for the effects appearing at least at the third order in dipole moments. The method is applied to the ground states of OH, OOH, HCOO, CN, CH, and PO radicals.

Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method

We present the analytic gradient theory and its pilot implementation for the multireference Brillouin-Wigner coupled cluster (BWCC) method and for the state-universal multireference coupled cluster method. The analytic gradient has been derived for three cases: (i) BWCC method without a size-extensivity correction, (ii) BWCC method with the iterative size-extensivity correction, and (iii) for the rigorously size-extensive state-universal method. The pilot implementation is based on full-configuration interaction expansions and is presently limited to single and double excitation levels; however, the resulting equations are general. For BWCC methods, they also do not contain terms explicitly mixing amplitudes of different reference configurations and can thus be implemented in an efficient way. The analytic gradients have been verified with respect to numerically computed ones on the example of CH2 molecule, and geometry optimizations of CH2 and SiH2 have been carried out.

Superluminal X-wave propagation: energy localization and velocity

The electromagnetic propagation of a Bessel-X wave is analyzed on the basis of a vectorial treatment in order to obtain information about the propagation of energy flux and the velocity of the energy. Knowledge of these quantities is of great interest since they are connected to the production of localized electromagnetic energy and to the topic of superluminality, respectively. The electric and magnetic fields are obtained in the far-field approximation by considering a realistic situation able to generate a Bessel-X wave. The vectorial treatment confirms the capability of this kind of wave to localize energy, while, quite surprisingly, even if the group velocity is superluminal, the energy velocity is equal to the light speed.

A constrained variational approach for energy derivatives in Fock-space multireference coupled-cluster theory

In this paper, we present a formulation based on constrained variational approach to enable efficient computation of energy derivatives using Fock-space multireference coupled-cluster theory. Adopting conventional normal ordered exponential with Bloch projection approach, we present a method of deriving equations when general incomplete model spaces are used. Essential simplifications arise when effective Hamiltonian definition becomes explicit as in the case of complete model spaces or some special quasicomplete model spaces. We apply the method to derive explicit generic expressions upto third-order energy derivatives for [0,1], [1,0], and [1,1] Fock-space sectors. Specific diagrammatic expressions for zeroth-order Lagrange multiplier equations for [0,1], [1,0], and [1,1] sectors are presented.

Energies and Dipole Moments of Excited States of Ozone and Ozone Radical Cation Using Fock Space Multireference Coupled-Cluster Analytical Response Approach

Using the Fock space multireference coupled-cluster (FS-MRCC) analytical linear response approach, we report the dipole moments of low-lying singlet and triplet excited states of ozone. The low-lying singlet and triplet excited states are calculated at the ground-state geometry and at the adiabatic geometry for the 1A2 and 1B1. For comparison we also calculate at the ground-state geometry the dipole moments of the 1A2, 1B1 and 1B2 using multireference configuration interaction (MRCI) with a bigger VQZ basis and complete active space. We also report as by-product the excitation energy values in the singles and doubles approximation. At the ground-state geometry we also report the energy and the dipole moments of the 2A1, 2A2 and 2B1 states of the ozone radical cation. The energy of the ozone cation radical is compared with the other correlated approaches. It matches well with the experimental values.