Nonunitary projective transcorrelation theory inspired by the F12 ansatz

An alternative nonunitary transcorrelation, inspired by the F12 ansatz, is investigated. In contrast to the Jastrow transcorrelation of Boys-Handy, the effective Hamiltonian of this projective transcorrelation features: 1. a series terminating formally at four-body interactions. 2. no spin-contamination within the non-relativistic framework. 3. simultaneous satisfaction of the singlet and triplet first-order cusp conditions. 4. arbitrary choices of pairs for correlation including frozen core approximations. We discuss the connection between the projective transcorrelation and F12 theory with applications to small molecules, to show that the cusp conditions play an important role to reduce the uncertainty arising from the nonunitary transformation

Coupled-cluster calculations of properties of Boron atom as a monovalent system

We present relativistic coupled-cluster (CC) calculations of energies, magnetic-dipole hyperfine constants, and electric-dipole transition amplitudes for low-lying states of atomic boron. The trivalent boron atom is computationally treated as a monovalent system. We explore performance of the CC method at various approximations. Our most complete treatment involves singles, doubles and the leading valence triples. The calculations are done using several approximations in the coupled-cluster (CC) method. The results are within 0.2-0.4% of the energy benchmarks. The hyperfine constants are reproduced with 1-2% accuracy

Monte Carlo explicitly correlated methods

Solving the non-relativistic time-independent electronic Schrödinger equation is in general difficult and requires approximation. For experimental accuracy, wave-function based methods require a large set of basis functions and inclusion of instantaneous correlation through expensive correlated methods. The methods that have been developed to account for the incompleteness of the basis set, the R12/F12 methods, create high dimensional integrals that need to be separated with the resolution of the identity, are limited in their form of the correlation factor due to analytical integration, and not highly parallel scalable. The solution to these drawbacks proposed in this work is Monte Carlo (MC). The stochastic second-order many-body perturbation theory, or the MC-MP2-F12 method, was developed for highly parallel evaluation of second-order many-body perturbation theory (MP2) energies near the complete basis set (CBS) limit. Single molecule energies were on average closer to the CBS limit than the corresponding method with a much larger basis set. Many different reaction energies for small molecules were computed showing a mean error from the CBS limit result within chemical accuracy. Two different methods were used the full variational MP2-F12 correction, MC-MP2-F12($VBX$), and a non-variational approximate form only satisfied at the minimum of the MC-MP2-F12($VBX$) formula, MC-MP2-F12($V$). Despite previous assumptions, the MC-MP2-F12($V$) formula is accurate not only for absolute energies but relative energies as well. Scaling for relative errors was shown to be $O(n^{4})$ where $n$ is the number of basis functions, one order lower than the corresponding deterministic method. Due to the MC-MP2-F12($V$) and more complete MC-MP2-F12($VBX$) having the same asymptotic scaling as $n$ increases, it is generally recommended that one use the $VBX$ method for larger molecules. Various correlation factors were tested but the Slater-type geminal (STG) developed by Ten-no was confirmed to be the best. A more extensive study of different functional forms of correlation factors was conducted using the MC-MP2-F12 method with a total of 17 correlation factors in order to elucidate qualities of the correlation hole and shape. Higher-order cusp conditions, or derivatives of the wavefunction, and their properties were also studied. It was found that every correlation factor that had the best convergence to the CBS limit had a very specific shape on the range of 0 to 1.5 Bohr. Despite having vastly differing long-range behavior, the best correlation factors gave very similar energies. This was found to be due to the decoupling of electrons at long distance, and the dominance of the orbital expansion at large inter-electron distance, $r_{12}$. While the importance of satisfying the cusp condition at $r_{12}=0$ could not be determined, the study confirmed that the intermediate region is of the most importance in general. Lastly, the MC-F12 algorithm developed for MC-MP2-F12 was extended to explicitly correlated second-order Green's function theory (GF2-F12) for basis-set corrected ionization potentials (IPs). The same set of benchmark organic molecules that were studied in the original GF2-F12 study were compared to verify the usefulness of the MC algorithm. Analogous to MC-MP2-F12, the two different methods MC-GF2-F12($V$) and MC-GF2-F12($VBX$) were tested. A mean average error of 0.049 eV and 0.018 eV was achieved for the MC-GF2-F12($V$) and MC-GF2-F12($VBX$) methods respectively. System size scaling was found to be $O(n^{4})$. As a demonstration of size scalability, the first IPs of fullerenes C$_{60}$ and C$_{70}$ were corrected from HF at the MC-GF2-F12($VBX$) level. Errors of 0.37 eV and 0.05 eV from experiment were achieved for C$_{60}$ and C$_{70}$ respectively. The sources of the large error in C$_{60}$ is unknown. Further accuracy can be expected from developing the full non-diagonal frequency-dependent formalism with MC, as well as combining MC-GF2-F12 with the MC-GF3 and MC-GF4 methods

New model Hamiltonians for improved orbital basis set convergence

The standard approach in quantum chemistry is to expand the eigenfunctions of the non relativistic Born Oppenheimer Hamiltonian in terms of Slater determinants. The quality improvements of such wavefunctions in terms of the underlying one electron basis is frustratingly slow. The error in the correlation energy decreases only with L 3 where L is the maximum angular momentum present in the basis. The integral evaluation effort that grows with 0(N4) prevents the use of ever larger bases for obtaining more accurate results. Most of the developments are therefore focused on wavefunction models with explicit correlation to get faster convergence. Although highly successful these approaches are computationally very demanding. A different solution might be provided by constructing new operators which take care of the information loss introduced by truncating the basis. In this thesis different routes towards such new operators are investigated.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

New model Hamiltonians for improved orbital basis set convergence

The standard approach in quantum chemistry is to expand the eigenfunctions of the non relativistic Born Oppenheimer Hamiltonian in terms of Slater determinants. The quality improvements of such wavefunctions in terms of the underlying one electron basis is frustratingly slow. The error in the correlation energy decreases only with L 3 where L is the maximum angular momentum present in the basis. The integral evaluation effort that grows with 0(N4) prevents the use of ever larger bases for obtaining more accurate results. Most of the developments are therefore focused on wavefunction models with explicit correlation to get faster convergence. Although highly successful these approaches are computationally very demanding. A different solution might be provided by constructing new operators which take care of the information loss introduced by truncating the basis. In this thesis different routes towards such new operators are investigated.EThOS - Electronic Theses Online ServiceGBUnited Kingdo