Excitation energies and response properties of molecules using internally contracted multireference coupled cluster methods

Abstract

Calculation of molecular properties is one of the most important aspects of quantum chemistry. The response theory, which is a general framework applied to different electronic structure methods, is widely used to calculate several static and frequency-dependent molecular properties. In response theory, properties are obtained as the response of an electronic state to the external perturbations like electromagnetic field. Several electrical properties, like dipole moment and frequency-dependent polarizability, along with different magnetic properties like magnetizability and electronic g-tensor can be evaluated following this formalism. Response theories have been developed for single reference methods, such as the coupled cluster method and they are routinely used for calculating molecular properties for closed-shell molecules. However, there is no well-established method to calculate these molecular properties for multireference systems where more than one determinant is used as the zeroth order reference. This thesis aims to develop a response formalism for internally contracted multireference coupled cluster (ic-MRCC) method in order to calculate highly accurate properties for multireference systems. ic-MRCC has been developed and used successfully, in recent years, to calculate energies with very high accuracy for different kinds of multireference systems such as open-shell molecules, dissociating bonds and transition metal compounds. As the first step of the response formalism, a time-dependent Lagrangian is formulated for the ic-MRCC theory. Formulation of this Lagrangian introduces Lagrange multipliers as a new set of parameters. The first derivative of the Lagrangian with respect to the perturbation produces the expression for the first order properties as an expectation value. Equations to obtain the zeroth order Lagrange multipliers, which are required to calculate the first order properties, are also formulated. A second derivative of the Lagrangian gives the linear response function as a function of the frequency of the external perturbation. The response equations are formulated and solved to get the first order wave function parameters which are used in evaluating this linear response function. Frequency-dependent second-order properties are obtained as the values of this linear response function for different frequencies. Poles of the linear response function represent the excitation energies of molecules. The excitation energies are thus obtained for ic-MRCC by finding these poles of the response function. But, the linear response function, as obtained from the formulation of response theory for ic-MRCC, gives unphysical second-order poles. The appearance of these second-order poles is avoided through approximations while obtaining both the second order properties and the excitation energies. Results obtained from these approximated versions of the ic-MRCC response formulation do not show any other spurious poles, like some other MRCC methods, as ic-MRCC deals with a linearly independent excited space. This response formulation is applied to calculate several molecular properties and corresponding results are presented. Electrical properties such as dipole moments, quadrupole moments and electric field gradients, along with the spin-dependent properties, such as hyperfine coupling constants, are calculated as the expectation values. On the other hand, the second order properties, such as the frequency dependent electrical polarizabilities, are calculated from the expression of the linear response function. Excitation energies are also calculated for several molecules and compared with the results obtained from other quantum chemical methods. All these results show that ic-MRCC provides very accurate properties and excitation energies for different multireference systems.