Spectroscopy and Dynamics of the Predissociated, Quasi-linear S2 State of Chlorocarbene

In this work, we report on the spectroscopy and dynamics of the quasi-linear S2 state of chlorocarbene, CHCl, and its deuterated isotopologue using optical-optical double resonance (OODR) spectroscopy through selected rovibronic levels of the S1 state. This study, which represents the first observation of the S2 state in CHCl, builds upon our recent examination of the corresponding state in CHF, where pronounced mode specificity was observed in the dynamics, with predissociation rates larger for levels containing bending excitation. In the present work, a total of 14 S2 state vibrational levels with angular momentum ℓ = 1 were observed for CHCl, and 34 levels for CDCl. The range of ℓ in this case was restricted by the pronounced Renner-Teller effect in the low-lying S1 levels, which severely reduces the fluorescence lifetime for levels with Ka \u3e 0. Nonetheless, by exploiting different intermediate S1 levels, we observed progressions involving all three fundamental vibrations. For levels with long predissociation lifetimes, rotational constants were determined by measuring spectra through different intermediate J levels of the S1 state. Plots of the predissociation linewidth (lifetime) vs. energy for various S2 levels show an abrupt onset, which lies near the calculated threshold for elimination to form C(3P) + HCl on the triplet surface. Our experimental results are compared with a series of high level ab initio calculations, which included the use of a dynamically weighted full-valence CASSCF procedure, focusing maximum weight on the state of interest (the singlet and triplet states were computed separately). This was used as the reference for subsequent Davidson-corrected MRCI(+Q) calculations. These calculations reveal the presence of multiple conical intersections in the singlet manifold

Robust methods for construction of global potential energy surfaces

This thesis is about the development of robust methods for construction of global potential energy surfaces to study the spectroscopy and dynamics of molecular systems. A potential energy surface represents the electronic energy of a molecule as a function of its geometry. This is central to how chemists view molecular systems in terms of motion across a rich energy landscape where barriers separate wells corresponding to different stable structures. The range of molecular distortions defines the potential energy surface. Computing the potential energy surface of a molecule has become a fundamental operation in modern theoretical chemistry studies. The Born-Oppenheimer approximation simplifies the Schrödinger equation (since the nuclei move slowly relative to the electrons), and enables computation of energies forming the surface. In order to develop a highly accurate surface, it is generally required to compute energies at many (typically thousands) molecular geometries. These data are then fit together using an interpolative scheme to form an analytic function. Due to interaction between states, in order to develop a surface for a particular state of interest, one often needs to include several states. In a multistate calculation, states are optimized for some choice of relative weights. It is necessary to dynamically adjust the weights, as the geometry is varied, in order to obtain a smooth and continuous surface (as using fixed weights can lead to disruptive discontinuities where states switch character). This project developed a weighting scheme based on an energy dependent functional designed to produce high accuracy and robust convergence for global surfaces. This method has been successfully demonstrated on ozone. The theoretical calculations are in good agreement with experiments, producing a significant improvement of the rate constant for the O + O₂ exchange reaction --Abstract, page iii

Construction of multi-state potential energy surfaces for spectroscopy and dynamics

This dissertation is about construction and visualization of multi-state Born-Oppenheimer potential energy surfaces which are essential for studying spectroscopy and dynamics. A potential energy surface is a mathematical function that represents the energy of a system as a function of its molecular geometry. The Born-Oppenheimer approximation enables us to solve the Schrödinger equation by separating the nuclear and electronic motions. Construction of potential energy surfaces has become a basic and crucial operation for chemists in order to compute various electronic states of molecules for understanding the spectroscopy, kinetics and dynamics of molecules. These methods have been used to successfully (i) predict transitions, spectroscopic constants and band origins for magnesium carbide (MgC) and (ii) calculate global spin-orbit surfaces in order to assign levels in the mono-halocarbenes, CH(D)X (X=Cl, Br, I). 3D plastic models of the potential energy surfaces were also generated using additive manufacturing (3D printing) for understanding the reactivity and stable structures of molecules --Abstract, page iv

A Density Functional Theory for the Average Electron Energy

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn-Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations

MODELING SPIN-ORBIT COUPLING IN THE HALOCARBENES

Halocarbenes are organic reactive intermediates with a neutral divalent carbon atom that is covalently bonded with a halogen and another substituent. Being the smallest carbenes that exhibit closed shell ground states, they have contributed greatly to our understanding of the reactivity of singlet carbene species and the factors that contribute to singlet-triplet energy gaps. We report an analysis of spin-orbit coupling in the mono-halocarbenes, CH(D)X, where X = Cl, Br, I. Single Vibronic Level (SVL) emission spectroscopy and Stimulated Emission Pumping (SEP) spectroscopy have been used to probe the ground vibrational level structures in these carbenes which have indicated the presence of perturbations involving the low-lying triplet state. In this talk, we present two approaches to model these interactions. Anharmonic constants, singlet-triplet gaps and geometry-dependent spin-orbit (SO) coupling surfaces were computed using high-level explicitly correlated methods such as CCSD(T)-F12b and MRCI-F12. These were used to evaluate SO coupling matrix elements and hence predict/fit mixed-perturbed singlet-triplet experimental levels. Results are also compared to those from a simpler model using a geometry-independent SO-constant

Accelerating variational quantum eigensolver convergence using parameter transfer

One impediment to the useful application of variational quantum algorithms in quantum chemistry is slow convergence with large numbers of classical optimization parameters. In this work, we evaluate a quantum computational warm-start approach for potential energy surface calculations. Our approach, which is inspired by conventional computational methods, is evaluated using simulations of the variational quantum eigensolver. Significant speedup is demonstrated relative to calculations that rely on a Hartree-Fock initial state, both for ideal and sampled simulations. The general approach of transferring parameters between similar problems is promising for accelerating current and near-term quantum chemistry calculations on quantum hardware, and is likely applicable beyond the tested algorithm and use case

Towards a Global Model of Spin-orbit Coupling in the Halocarbenes

We report a global analysis of spin-orbit coupling in the mono-halocarbenes, CH(D)X, where X = Cl, Br, and I. These are model systems for examining carbene singlet-triplet energy gaps and spin-orbit coupling. Over the past decade, rich data sets collected using single vibronic level emission spectroscopy and stimulated emission pumping spectroscopy have yielded much information on the ground vibrational level structure and clearly demonstrated the presence of perturbations involving the low-lying triplet state. To model these interactions globally, we compare two approaches. First, we employ a diabatic treatment of the spin-orbit coupling, where the coupling matrix elements are written in terms of a purely electronic spin-orbit matrix element which is independent of nuclear coordinates, and an integral representing the overlap of the singlet and triplet vibrational wavefunctions. In this way, the structures, harmonic frequencies, and normal mode displacements from ab initio calculations were used to calculate the vibrational overlaps of the singlet and triplet state levels, including the full effects of Duschinsky mixing. These calculations have allowed many new assignments to be made, particularly for CHI, and provided spin-orbit coupling parameters and values for the singlet-triplet gaps. In a second approach, we have computed and fit full geometry dependent spin-orbit coupling surfaces and used them to compute matrix elements without the product form approximation. Those matrix elements were used in similar fits varying the anharmonic constants and singlet-triplet gap to reproduce the experimental levels. The derived spin-orbit parameters for carbenes CHX (X = Cl, Br, and I) show an excellent linear correlation with the atomic spin-orbit constant of the corresponding halogen, indicating that the spin-orbit coupling in the carbenes is consistently around 14% of the atomic value

Benchmarking the Variational Quantum Eigensolver through Simulation of the Ground State Energy of Prebiotic Molecules on High-Performance Computers

We use the Variational Quantum Eigensolver (VQE) as implemented in the Qiskit software package to compute the ground state energy of small molecules derived from water, H$_2$O, and hydrogen cyanide, HCN. The work aims to benchmark algorithms for calculating the electronic structure and energy surfaces of molecules of relevance to prebiotic chemistry, beginning with water and hydrogen cyanide, and to run them on the available simulated and physical quantum hardware. The numerical calculations of the algorithms for small quantum processors allow us to design more efficient protocols to be run in real hardware, as well as to analyze their performance. Future implementations on accessible quantum processing prototypes will benchmark quantum computers and provide tests of quantum advantage with heuristic quantum algorithms.Comment: 9 pages, 3 figures, 4 tables, MIPT2020, Moscow, 7-11 September 2020, AIP Proceedings (Table III corrected; ref. [16] updated

Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry

Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on current and near-term devices. REM can be applied alongside existing mitigation procedures, while requiring minimal postprocessing and only one or no additional measurements. The approach is agnostic to the underlying quantum mechanical ansatz and is designed for the variational quantum eigensolver. Up to two orders-of-magnitude improvement in the computational accuracy of ground state energies of small molecules (H2, HeH+, and LiH) is demonstrated on superconducting quantum hardware. Simulations of noisy circuits with a depth exceeding 1000 two-qubit gates are used to demonstrate the scalability of the method