Ajit Banerjee

Applications of multiconfigurational coupled‐cluster theory

A coupled‐cluster method which permits the use of multiconfiguration reference states has recently been developed in this laboratory. In the present work, it is applied to several states of H2 (1Σg+), Li(2S), HeH2(1A1), and CH2(3B1,1A1), which include both open and closed shells. These applications are made within an approximation in which the cluster operator (T) is truncated at T2, T≃T1+T2 and the expansion of e−THeT is truncated at the double‐commutator level. For cases where a single configuration function ceases to be a good starting point, it is found that a single configuration based truncated coupled‐cluster procedure may exhibit serious difficulties. In such cases we find it possible to choose a multiconfigurational reference state for which our coupled‐cluster procedure converges reasonably rapidly. This paper contains several illustrations of such convergence characteristics.

Excess electrons in condensed media: Theory of optical absorption spectrum in molecular solutions

A theoretical formalism is developed for analyzing the spectra of excess electrons in pure molecular solids and liquids. A perturbation decomposition of the Hamiltonian allows the expression for the band shape I (ω) to be written as a sum of a zeroth order part, proportional to dipole transition matrix elements and corresponding Franck–Condon factors, and perturbation terms containing effects of electron hopping and their fluctuations. By using several physically motivated approximations (e.g., the temporally localized nature of electronic transitions which allows a short‐time expansion of the time dependence of operators), the expression for I (ω) can be expressed in terms of solvent structure information and the electron–solvent interaction potential. From the general expressions for I (ω) a simplified model was developed in the special case of systems for which bound‐to‐bound transitions are dominant. This model has been successfully applied to the spectra of excess electrons in ethanol and anthracene ...

A theoretical and experimental study of Sb4O6: vibrational analysis, infrared, and Raman spectra

The first ab initio theoretical study of tetraantimony hexoxide (Sb4O6) is reported. The normal mode frequencies, intensities, and the corresponding vibrational assignments of Sb4O6 in T(d) symmetry were calculated using the GAUSSIAN 98 set of quantum chemistry codes at the Hartree-Fock (HF)/CEP-121G, Møller-Plesset (MP2)/CEP-121G, and density functional theory (DFT)/B3LYP/CEP-121G levels of theory. By comparison to experimental data deduced by our laboratory and others, correction factors for the calculated vibrational frequencies were determined and compared. Normal modes were decomposed into three non-redundant motions (Sb-O-Sb stretch, Sb-O-Sb bend, and Sb-O-Sb wag). Percent relative errors found for the HF, DFT, and MP2 corrected frequencies when compared to experiment are 5.8, 6.1, and 5.7 cm(-1), respectively. Electron distributions for selected molecular orbitals are also considered.

A test of multiconfigurational coupled-cluster theory on Be(1S)+H2(X 1Σg+) → BeH2(1A1)

Abstract A perpendicular C2v insertion of Be into H2 is explored via our multiconfiguration coupled-cluster method within the double-excitation (CCMC-T2) model. This straight-line path, which encompasses the fragment geometry (Be and H2), the equilibrium geometry (linear BeH2) and a transition-state geometry of BeH2, requires several configurations to achieve a qualitatively correct zeroth-order description of the ground state. The path is identical to that used by Shepard et al. in their single-configuration coupled-cluster study of this same system. It is demonstrated that the CCMC-T2 model is theoretically and computationally viable and that the resultant coupled-cluster energies parallel the reference-wavefunction energies. When the reference wavefunction ceases to incorporate the dominant configurations, the coupled-cluster wavefunction correspondingly represents the state poorly.

Multiconfiguration coupled-cluster calculations for excited electronic states: Applications to model systems

Abstract A multiconfigurational coupled-cluster method previously developed in our laboratory is used to study excited states of the same spatial and spin symmetry as the ground state. Applications are made, with rather small atomic orbital basis sets, to molecular systems which are highly correlated. These small-basis calculations are viewed on model calculations whose value lies in the fact that one can also obtain the exact (full configuration interaction) energy in such cases. The results show that even though the coupled-cluster equations may have many spurious solutions, one can locate solutions corresponding to the desired excited states by using procedures similar to those utilized for ground states. To achieve this success, one should include in the reference function all of the dominant configurations of the state under consideration. Next, one should use the unique solution of the linearized coupled-cluster equations as the initial estimate to begin the solution of the non-linear coupled-cluster equations. If the solution of these non-linear equations gives rise to one or more large t amplitudes one should repeat this procedure but with the configuration corresponding to the large t amplitude included in the reference function.

Theoretical study of lithium intercalated graphite

We have performed a series of calculations on small models (number of atoms ranging from 10 to 34) of graphite and lithium intercalated graphite (LIG) at the UHF level with a minimal basis set for the valence electrons and an effective core potential for the core electrons (CEP‐4G), where the basis and the CEP is optimal for free atoms. We have shown that small model hosts, such as C10 (Bernal i.e., AB) and C12 (primitive hexagonal, i.e., AA), enable us to make several predictions regarding LIG. Firstly, lithium looses its valence electron upon entering either type of host lattice and eventually falls into a body‐centered position in an AA host lattice. Secondly, lithium strongly destabilizes the AB lattice, while it strongly stabilizes the AA lattice. Thirdly, the barrier for site hopping in the limit of infinite dilution (Ea) can be estimated along with a related quantity which we call the hilltop energy (see text). Further, we have shown that by building up to host models no larger than C32 (AA) we can...

Monte Carlo simulation of small hydrate clusters of NO−2

The ground‐state Hartree–Fock (HF) potential for the NO−2:H2O dimer has been computed for 102 different intermolecular geometrical configurations and has been expressed in a computationally convenient analytical form. The main conclusion drawn from these calculations is that the ion–solvent attraction is mainly electrostatic for intermolecular distances between 6.0 and 7.0 bohr (N‐to‐O distance). Keeping the dipole vector of the H2O molecule oriented toward the NO−2 ion yields energetically favorable conformations. Rotations of the H2O molecule which do not change the dipole orientation of the H2O have been found to have small barriers (∼4 kcal/mole), whereas those that destroy proper dipole alignment encounter large (∼30 kcal/mole) barriers. The use of such ion–H2O intermolecular potentials together with the H2O:H2O pair potential of Clementi permits Monte Carlo techniques to be used to examine the nature of the inner hydration shells of NO−2. The results of Monte Carlo simulations of NO−2(H2O)n1⩽n⩽15 ar...

MC SCF molecular gradients and hessians: Computational aspects

Abstract Molecular gradients and hessians for multiconfigurational self-consistent-field wavefunctions are derived in terms of the generators of the unitary group using exponential unitary operators to describe the response of the energy to a geometrical deformation. Final expressions are cast in forms which contain reference only to the primitive non-orthogonal atomic basis set and to the final orthonormal molecular orbitals; all reference to intermediate orthogonalized orbitals is removed. All of the deformation-dependent terms in the working equations reside in the one- and two-electron integral derivatives involving the atomic basis orbitals. The deformation-independent terms, whose contributions can be partially summed, involve symmetrized density matrix elements which have the same eight-fold index permutational symmetry as te one- and two-electron integral derivatives they multiply. This separation of deformation-dependent and -independent factors allows for single-pass integral-derivative-driven implementation of the gradient and hessian expressions.

Translational and rotational symmetries in integral derivatives

Based upon the invariance under translations and rotations of quantum chemical one‐ and two‐electron integrals, a method for obtaining a complete set of independent relations among integral derivatives is presented. Due to the unitary form of the operators corresponding to finite translations and rotations, this analysis is generally applicable to all orders of integral derivatives. It is shown that the number of dependent integral derivatives is equal to the number of such independent relations. These dependent integral derivatives can thus be straightforwardly determined in terms of the remaining derivatives which must be explicitly calculated. For example, out of a total of 21, 45, and 78 second‐derivative integrals for the two‐ , three‐ , and four‐center cases, respectively, only 1, 6, and 21 such integral derivatives need be explicitly calculated. The set of such independent and dependent integral derivatives can be chosen in a manner which imposes no restrictions on the allowable geometries of the n...

A multiconfiguration self‐consistent‐field group function method for problems with repeating potentials

An implementation of a conceptual scheme for performing a finite‐cluster electronic structure calculation so as to simulate, within the finite cluster, an extended periodic continuation of the cluster is reported. The implementation extends a scheme used previously at a single‐determinant wave function level of approximation to a multiconfiguration self‐consistent‐field (MCSCF) level. The total wave function has the form of McWeeny’s group functions. The MCSCF working equations are cast in the exponential‐i‐lambda language (EIL) and the energy expressions are cast in notation of the graphical unitary group approach (GUGA). The modifications to the MCSCF working equations necessary to do group function calculations are also developed in the GUGA–EIL notation. A procedure for wave function transfer from one unit of the cluster to another is described. All of this conceptual scheme has been put together in working computer algorithms and applied to two informative, illustrative systems, Be2, and finite hydro...