M. Durga Prasad

Use of a size-consistent energy functional in many electron theory for closed shells

If the ground state wave-function ψgr is written as ψgr = Φo+X, withX as the correlation part satisfying (φo¦x) = 0, andx expressed as an expansion in terms of pair, pair-pair etc. cluster functions, then the expectation value of the energyE = (ψgr¦H¦ψgr)/(ψgr¦ψgr) has the property that the normalization term in the denominator completely cancels the unlinked part of the numerator, as noted by Sinanoglu. We use Cizeks coupled-pair ansatz ψgr = exp(T2)Φ0 for transcribing Sinanoglus expansion in a many-body language to study the behaviour of the size-consistent (linked) energy functional thus generated. For calculating the matrix-elements of the cluster components ofT, we use two recipes: (1) a variational determination of the cluster components using Eulers principle for the energy functional akin in spirit to the Varied Portion Approach (VPA) of Sinanoglu and (ii) a nonvariational determination of the cluster components using the conventional coupled-cluster theory. Results are presented for model test systems and are compared with variational CI and nonvariational coupled-cluster values. It has been observed that the values obtained from the size-consistent energy functional from the cluster components obtained from methods (i) and (ii) are quite close and both compare well with the nonvariational coupled-cluster results. Some useful simplifications afforded by the VPA are also indicated. A brief perspective of the method vis-a-vis other related theories is also given.

Molecular applications of open-shell coupled cluster theory for energy difference calculations: ionization and Auger spectra of F2

Abstract The first ab initio molecular applications of our open-shell coupled cluster (CC) method for direct calculation of energy differences are reported. Starting from the zero-valence ground-state problem, various one-, two-, ⋯ m -valence problems are hierarchically generated. Ionization and Auger spectrum calculations for F2 illustrate typical one- and two-valence situations. Particular attention is paid to generate alternative solutions corresponding to satellite peaks in the IP by exploiting the non-linear nature of the CC equations. The results are encouraging.

Coupled cluster description of anharmonic molecular vibrations. Application to O3 and SO2

Abstract The coupled cluster method is applied to the calculation of vibrational levels of O3 and SO2 and compared with the self consistent field approximation (SCF) and accurate quantum calculations. It is found that CCM truncated at the S4 level provides a marginally better description than SCF for the ground and low-lying excited states.

Calculation of vibrational energy of molecule using coupled cluster linear response theory in bosonic representation: Convergence studies

Vibrational excited state energies have been calculated using vibrational coupled cluster linear response theory (CCLRT). The method has been implemented on formaldehyde and water molecule. Convergence studies have been shown with varying the cluster operator from S(4) to S(6) as well as the excitation operator from four bosons to six bosons. A good agreement with full configuration interaction results has been observed with S(6) truncation at coupled-cluster method level and six bosonic excitations at CCLRT level.

Time‐dependent coupled cluster method: A new approach to the calculation of molecular absorption spectra

The time‐dependent coupled cluster method is developed to provide a formally exact theory of quantum‐mechanical motion of a vacuum state on multidimensional anharmonic surfaces with a view to calculate the molecular absorption spectra. The exact time evolution operator is represented as an exponential of creation operators. Since the separability requirments of many‐particle systems are built into such an ansatz, it is possible to develop approximations which can take into account any number of modes with much less computational effort than in a calculation by basis‐set expansion. The method gives a closed set of equations for harmonic surfaces and finite ordered equations for anharmonic surfaces when truncated at some finite rank.

Self-consistent-field dynamics of a model non-adiabatic system

Abstract The dynamics of a two-state three-mode model non-adiabatic system mimicking the S 1 , S 2 surfaces of pyrazine is studied under the time-dependent self-consistent-field (TDSCF) approximation. It is found that the TDSCF provides a good description for short time dynamics and suffices for calculating spectral features but is inadequate at longer times when vibrational dephasing becomes important.

Time‐dependent coupled cluster approach to multimode vibronic dynamics

The time‐dependent coupled cluster method is used to calculate the dynamics on coupled surfaces. The time‐dependent self‐consistent‐field solution of the initial doorway state is used as the reference state. Autocorrelation functions and spectra of two model systems are presented. It is found that the spurious recurrences in the self‐consistent‐field autocorrelation functions are eliminated in the coupled cluster approach and the spectral features are correctly reproduced at T=T1+T2 level of approximation.

A thermal self-consistent field theory for the calculation of molecular vibrational partition functions

A new approach for the calculation of anharmonic molecular vibrational partition functions is developed based on a separable ansatz to the thermal density matrix. The parameters appearing in the effective single particle Hamiltonians that generate the thermal density matrices are determined variationally. The resulting equations are the thermal analogs of the vibrational self-consistent field approximation. The method has the formal property that the free energy calculated by this approach is an upper bound to the exact free energy. Thermodynamic quantities calculated by this approach are generally in good agreement with the results of numerically converged calculations. This approach is more efficient than the standard sum over state approaches in that the computational resources scale with N(4) where N is the number of vibrational degrees of freedom. Thus it can be applied to fairly large systems.

The time-dependent coupled cluster approach to molecular photodissociation dynamics

Abstract The time-dependent coupled cluster method (TDCCM) has been applied to the photodissociation dynamics of linear triatomics using the Beswick—Jortner model. The autocorrelation function and absorption spectra have been evaluated and the convergence of the method has been tested by evaluating the autocorrelation function at different truncations of the S -matrix elements. It is found that the TDCCM approach converges to exact results quite quickly.

Molecular applications of coupled-cluster-based linear response theory: Inner and outer valence ionization potentials of nitrogen and water

Abstract We report the first ab initio molecular applications of our recently formulated linear response theory in the coupled-cluster framework for calculating inner and outer valence ionization potentials (IPs). The response model utilizes the coupled-cluster representation for the ground state Ψ gr and calculates the linear response of Ψ gr as it is subjected to the coupling of a photon field of frequency ω which destroys an electron. The poles of the response function provide the IPs. Applications to H 2 O and N 2 show encouraging results.