Sourav Pal

Use of Cluster Expansion Methods in the Open-Shell Correlation Problem

Publisher Summary This chapter discusses the developments of the open-shell many-body cluster expansion theories. Interpretation of most of the spectroscopic and dynamical phenomena, involving excited or ionized molecules and molecular fragments require models for open-shell states transcending the simple orbital description. The language of occupation number representation, coupled with the hole-particle description of the operators, the use of Wicks theorem and the attendant diagrammatic depiction of the various terms makes the many-body approach a very attractive alternative to the traditional CI-based theories. The open-shell many-body perturbation theory (MBPT) and the propagator or the Greens function methods have now developed into vast computational technology, generating softwares that are cost-effective and competitive with the CI-based codes. The cluster expansion based open-shell many-body formalisms possess even greater potentiality since they not only share and embed all the desirable features and technical advantages of the open-shell MBPT or propagator theories, but also are inherently non-perturbative in nature. They provide more compact descriptions of the electron correlation and are more flexible. Moreover, the cluster expansion of the open-shell functions provides valuable insight regarding the structure of general many-electron wave-functions.

On non-negativity of Fukui function indices

In this paper we have analyzed the factors which cause Fukui function (FF) indices to be negative, when evaluated in condensed form through crude finite difference approximation. Inability to take care of the relaxation effect and improper charge partitioning techniques have been cited to be the probable reasons. For the first time, we have shown that the “stockholders” charge partitioning technique (i.e., Hirshfeld’s analysis) produces non-negative FF values which, when evaluated through other kinds of charge partitioning techniques, become negative in some cases. Advantages of “stockholders” charge partitioning over other kinds of partitioning techniques are also discussed, particularly in case of evaluation of condensed FF.

Mulliken population analysis based evaluation of condensed Fukui function indices using fractional molecular charge

A thorough study on the nature of Mulliken population analysis (MPA) based condensed Fukui function (FF) indices has been performed. It is claimed analytically that nothing can be predicted about the sign of condensed FF indices, even when evaluated by using very small fractional molecular charge (i.e., approximately following the analytical definition of FF indices). The corresponding numerical demonstrations on different chemical systems confirm our claim.

Aromaticity and antiaromaticity of LixAl4 clusters: Ring current patterns versus electron counting

Maps of magnetic-field induced current density are computed for a series of lithium–aluminium clusters based on the planar Al4 cycle: formal 2π systems LiAl4− (C4v), Li2Al4 (D4h, Cs), and formal 4π systems Li3Al4− (Cs), and Li4Al4 (C2h). All four species sustain a diatropic σ ring current in the Al4 cycle. In the 2π systems, although the 4n + 2 π electron count suggests aromaticity and hence diatropicity, the π orbital is magnetically inactive, as in the Al42− dianion. However, in the 4π formally antiaromatic systems, the π-like HOMO supports an additional paratropic current. Considerations of orbital symmetry and energy, but not electron counting alone, rationalise both computed currents. All calculations were carried out at the coupled Hartree–Fock level in a 6-31G** basis using the CTOCD-DZ (continuous transformation of origin of current density – diamagnetic zero), or ipsocentric, formulation of magnetic response, where current density at any point is obtained with that point itself chosen as the origin of vector potential.

Multireference coupled cluster based analytic response approach for evaluating molecular properties: Some pilot results

In this paper we present the first results for linear response theory in the multireference Fock space framework. Dipole moments of the open shell radicals hydro peroxy radical, hydroxyl radical, and formyloxyl radical are discussed in this paper. The results obtained from the analytic response are compared with the experimental as well as the finite field results including relaxation of the orbitals and the results suggest that the effects of relaxation are substantial. The Fock space approach enables us to obtain the properties of excited states of these radicals in a single calculation. The dipole moments of the first excited states of the above radicals are also reported. The results of the lower Fock space sector energy derivatives are also presented.

Equation-of-motion coupled-cluster method for the study of shape resonance

The equation-of-motion coupled-cluster method (EOM-CC) is applied for the first time to calculate the energy and width of a shape resonance in an electron-molecule scattering. The procedure is based on inclusion of complex absorbing potential with EOM-CC theory. We have applied this method to investigate the shape resonance in e(-)N(2), e(-)CO, and e(-)C(2)H(2).

Nonlinear molecular properties using biorthogonal response approach

In this paper, we report the use of extended coupled cluster functional of Arponen, Bishop, and co‐workers to implement a stationary biorthogonal response approach. The objective of this is to calculate nonlinear molecular properties like hyperpolarizability, etc. in a more convenient way.

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.

A study of electronic and bonding properties of Sn doped Lin clusters and aluminum based binary clusters through electron localization function

We have carried out a thorough investigation of bonding and energetics in two different class of heteroatomic clusters viz. single impurity based LinSn (n⩽9) clusters and mixed aluminum-based binary clusters Al4X4 (X=Be, Mg, B, Si). We employ first principle Born–Oppenheimer molecular dynamics within the framework of density functional theory using generalized gradient approximation. The bonding characteristics have been analyzed using electron localization function (ELF) along with charge density and valence molecular orbital pictures. The analysis of bonding through ELF reveals that in LinSn (n⩽9) clusters there is a transition from ionic bond to a metallic bond through an intermediate ionic–metallic bond. On the other hand, it is found that Al4X4 (X=Be, Mg, B, Si) clusters show interesting characteristics of lone pairs on Al, polar covalent bonding, and a multicenter bonding. We demonstrate that ELF can play an important role in analyzing different types of bonding characteristics in heteroatomic clusters.

LITHIUM BONDING INTERACTION IN H2CY...LIF (Y=O,S) COMPLEXES : A THEORETICAL PROBE

Ab initio calculations at 6-31++G(d,p) level have been done on H2CY⋯LiF (Y=O,S) complexes choosing ten possible orientations in each complex. The effect of correlation on complex binding energies has been studied via single point MP2 (full) calculations done on 6-31++G(d,p) geometry. Binding energies have been corrected for basis set superposition error. Frequency calculations confirm that H2CO⋯LiF and H2CS⋯LiF complexes have three and two stable forms, respectively. The most stable form in each complex has been found to have a strong lithium bonding interaction and a secondary hydrogen bonding interaction. NBO analysis has revealed that in this form oxygen donates nσ lone pair while sulfur donates its nπ lone pair. In yet another stable form of these complexes, mixed donation of π and nσ electrons have been observed.