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Theoretical Molecular Science Laboratory
Department of Chemistry
Indian Institute of Technology Bombay
Research Area
In the framework of Theoretical Quantum Chemistry, our major research interests lie in developing novel Quantum Chemical methodologies for treating strongly correlated molecular systems. The current key focus areas are:
Methods beyond quantum chemistry 'gold-standard' for structure and stability of molecular clusters
Determination of molecular interaction energy requires accurate estimation of electronic correlation effects and dynamical screening of Coulomb interaction. Our research in this direction aims to develop a suite of such methods that can account for all the effects with a cheaper computational scaling than the existing quantum chemical gold-standard, without unduly sacrificing the accuracy. The method relies on a double similarity transformed effective hamiltonian, which induces the effects of triple and higher order excitations with a two-body parametrization of the wave-operator.
In a recent publication, we have demonstrated that for the hydrogen-bonded systems, the performance of our methods is superior than all other existing methods, and research is underway to assess its performance over different classes of molecular clusters.
Coupled cluster theory via nonlinear dynamics, synergetics and machine learning
Any nonlinear iterative process of multivariable optimization shows synergy among the iterable quantities, and so does coupled cluster (CC) theory. We established that the CC iteration process is dictated by a few "significant" cluster operators, mostly involving valence excitations, while all other amplitudes may be considered to be enslaved. We employ various supervised ML techniques to realize the master-slave dynamics, and express the enslaved dependent amplitudes in terms of the independent master amplitudes. We thus have come up with a hybrid CC-ML algorithm by dynamically reducing the effective degrees of freedom of the process. The algorithm has been proved to produce CC energy within micro-Hartree accuracy (to the exact canonical CC) with 45%-55% reduction in computational timings. The model is based on synergistic inter-dependency among the cluster amplitudes and does not require any prior training to generate the data set.
We have further extended this model to analytically determine the synergistic inter-dependence among the amplitudes. This has been achieved via decoupling of various amplitudes based on their relaxation time-scale to reach the fixed points. While an "adiabatic decoupling" has been proved to be very accurate and inexpensive, we are formulating post-adiabatic corrections which we believe would lead to have better accuracy with orders of magnitude savings in computational scaling.
Many body theories of molecules and extended systems with quantum computers
Quantum computers are equipped to solve for classically intractable many body systems. We are developing novel quantum phase estimation (QPE) algorithms to solve for strongly correlated many body states in a spin adapted manner. In our recent work, we had extended this formulation to take care of multi determinantal wavefunction. Our future work in this direction will also include a variational quantum eigen solver (VQE) which has emerged of late as the most robust method for solving quantum many body systems in a quantum computer. Our newly developed codes, interfaced with qiskit provide enough flexibility to try out different atomic, molecular and condensed phase systems.
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Fragment Molecular Orbital approach based Coupled Cluster Theory
Fragment Molecular Orbital (FMO) is a convenient technique to calculate the energetics of large molecules and clusters using first principle methods, which is otherwise not feasible using any conventional method. One may employ a physically motivated fragmentation scheme where a large chemical system is broken into several parts and determine energy of each fragment in a self consistent manner. In this project, we integrate our newly developed novel coupled cluster methods with FMO for accurate calculation of correlation energy of chemical systems. The FMO framework substantially reduces the computational cost of correlation calculation without unduly sacrificing the accuracy.
Coupled cluster based Linear Response treatment to calculate molecular properties
Following our earlier work, we are trying to implement a Linear Response formulation of our double similarity transformed cc theory which includes triples excitation to calculate excitation energy of different molecular systems by subjecting them to a external electric field. The method relies on the Lagrangian and first order differentiation of this with respect to the Lagrange multipliers produces the response equations. These response equations can be cast into a matrix equation. Now, at the poles, the external periodic field resonates with the response functions and make the matrix equation into a matrix eigenvalue equation. After diagonalizing this matrix, one can obtain the excitation energy directly as an eigenvalue.
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