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Developments in Auxiliary Field Quantum Monte Carlo for Molecules
This thesis presents a compilation of recent work on benchmarking, applying, and developing Auxiliary Field Quantum Monte Carlo (AFQMC) for use in ab initio simulations of the electronic structure of molecules.
With Chapter 1 I begin with a benchmark of phaseless AFQMC versus experiment in obtaining gas phase ligand dissociation energies of a set of tetrahedral and octahedral transition metal complexes. ph-AFQMC is shown to acquire chemical accuracy through the use of correlated sampling (CS) and CASSCF trial wave functions selected via a black box procedure.
This is followed in Chapter 2 with another gas phase benchmark of ph-AFQMC versus experiment, this time calculating the redox potentials for a set of metallocenes, where we find a mix of correlated sampling and large CASSCF trials necessary to reproduce gas phase experimental values to within 1.7 ± 1.0 kcal/mol. Additionally, the inclusion of QZ ph-AFQMC values, either using UHF or CASSCF trials, was found to be necessary for a few systems, as opposed to using a hybrid approach with alternate methods such as coupled cluster to extrapolate to the basis set limit.
In Chapter 3, having established protocols to obtain decent results on transition metal complexes with known experimental values, I apply ph-AFQMC to successfully predict the activity of a set of new annihilators for optical upconversion. For a set of functionalized anthracene molecules, I report agreement within statistics between ph-AFQMC and a localized approximation to coupled cluster singles doubles and perturbative triples (DLPNO-CCSD(T0)), and develop intuitive guidelines for tuning the excited state energies of anthracene. For a single molecule in an additional set of functionalized benzothiadiazole (BTD) molecules, Ph-BTD, ph-AFQMC and DLPNO-CCSD(T) disagree significantly; subsequent experimental testing validates the ph-AFQMC result.
In Chapter 4 I present an approach based on localized orbitals to reduce the scaling with system size from quartic to cubic for the energy evaluation, the functional bottleneck for the majority of AFQMC calculations. Additionally, I describe the practical implementation of such an algorithm to be run on large GPU clusters. This allows AFQMC to be run for both larger systems and trials at a significantly decreased cost, while still reproducing full AFQMC results within the statistics of the method.
With Chapter 5, I conclude with the development and characterization of a novel constraint, linecut (lc-) AFQMC, which exhbits distinct behavior versus the phaseless constraint. We demonstrate benchmarks for a variety of weakly to strongly correlated molecules for which we have the exact total energies, and observe that lc-AFQMC outperforms ph-AFQMC for the majority of systems studied.
I conclude with the description of a systematic method to remove the linecut constraint, partially removing the bias and re-introducing the fermionic sign problem while still maintaining a practicable signal to noise ratio. This allows for us to recover the exact energy of FeO with a fraction of the cost of converging the trial wave function within ph-AFQMC
Free radical rearrangements of cyclohexa-2,5-diene derivatives and strained polycyclic compounds
Esters of cyclohexa-2,5-diene-l-carboxylic acid were investigated to study the transfer of the labile bisallylic hydrogens (C-4) to give the cyclohexadienyl radical and then the subsequent decarboxylative stage to give R •, the driving force being the rearomatisation of the benzene ring. The undesirable reaction, whereby hydrogen is abstracted from C-1, was prevented by the introduction of a methyl group into this position. The cyclohexa-2,5-diene-l-carboxylic acids are readily prepared by a Birch type reduction of benzoic acid. All the esters derived from cyclohexa-2,5-diene-l-carboxylic acid, were examined by EPR spectroscopy and showed the cyclohexadienyl radical. No decarboxylation was evident by this technique. Also investigated, by EPR spectroscopy, were the acids with different substituents at C-1, showing that for acids with highly stabilised alkyl substituents, decomposition occurs. Esters reacted with N- bromosuccinimide showed some of the desired bromides, formed after CO2 loss from the cyclohexadienyl radical. Esters forming non-stabilised radicals on decarboxylation have given the intended products in lower yields. The esters have also been examined in reactions with acrylonitrile, addition being observed to varying degrees. The radicals generated from 9-hydroxy- and 9-bromo-pentacyclo-[4.4.0.0 ²·⁵.0 ³⋅⁸.0 ⁴·⁷]nonane (homocubane) and for the same derivatives of pentacyclo- [4.4.0.0 ²·⁵.0 ³⋅⁸.0 ⁴·⁷]]decane (basketane) were observed by EPR spectroscopy. In spite of their very large strain energies both radicals rearranged extremely slowly and unrearranged products were obtained from homolytic reactions in solution at temperatures below 150°C. At higher temperatures the 9-basketyl radical rearranged by a cascade of three beta-scissions, the ultimate product being l-(4-cyclobut-2-enyl)cyclohexa-2,4-diene. The 9-homocubyl radical did not rearrange even at 220°C. Several reasons why these cage radicals rearrange at least six orders of magnitude more slowly than the related cubylcarbinyl radical are discussed. Photobromination of basketane yielded a mixture of four tetrabromides which were formed by bimolecular homolytic substitution at every bridgehead. Norcubylcarbinyl radicals, that were generated by bromine abstraction from norcubylcarbinyl bromide, rearranged so rapidly that only the product of β-scission, 6-methylenebicyclo[3.1.1]hept-3-yl, could be observed by EPR spectroscopy. The rate constant for β-scission was estimated from the EPR experiments, and from reductions of norcubylcarbinyl bromide with tributyltin hydride, to be > 5x10⁹s-l at 298K. A series of 3-substituted bicyclo[l.l.l]pent-l-yl radicals, including the 3-fluoro-derivative, was generated by bromine atom abstraction from l-bromo-3-substituted- bicyclo[l.l.l]pentanes and examined by EPR spectroscopy. The exceptionally large hyperfine splittings obtained from magnetic nuclei of the 3-substituents indicated that crosscage electronic interactions were substantial in these species. Bromine atom abstraction by triethylsilyl radicals from l-bromo-3-fluorobicyclo[l.l.l]pentane was found to take place more rapidly than bromine abstraction from the unsubstituted parent, i.e. the fluorine substituent mediated a significant polar effect. Evidence was found of a novel disproportionation process in which the γ-fluorine atom was transferred from the 3-fluoro-radical to a triethylsilyl or to a second bicyclo[l.l.l]pent-l-yl radical; an analogous chlorine atom transfer process was found for the 3-chloro-radical. 4-Substituted bicyclo[2.2.2]oct-l-yl radicals were generated by bromine atom abstraction from the corresponding l-bromobicyclo[2.2.2]octanes and observed in solution by EPR spectroscopy. The EPR data indicated that 4-substituents exercised a significant effect at the radical centre, mainly by a through bond mechanism. 10-Substituted triptycyl radicals were generated in a similar way but showed no hfs from magnetic nuclei of the substituents. Bicyclo[2.2.2]oct-l-yl radicals were added to benzene, tert-butylbenzene and 1,3-di-tert-butylbenzene to give cyclohexadienyl radicals which were characterised by EPR spectroscopy. The bicyclo[2.2.2]oct-l-yl radical generated in rerr-butylbenzene showed exclusive meta addition with formation of the corresponding l-polycyclo-3-tert-butylcyclohexadienyl radical
Heats of formation of platonic hydrocarbon cages by means of high-level thermochemical procedures
Hydrocarbon cages are key reference materials for the validation and parameterization of computationally cost-effective procedures such as density functional theory (DFT), semiempirical molecular orbital theory, and molecular mechanics. We obtain accurate total atomization energies (TAEs) and heats of formation (ΔfH°298) for platonic and prismatic hydrocarbon cages by means of the Wn-F12 explicitly correlated thermo-chemical protocols. We consider the following kinetically stable (CH)n polycyclic hydrocarbon cages: (i) platonic hydro-carbons (tetrahedrane, cubane, and dodecahedrane), (ii) prismatic hydrocarbons (triprismane, cubane, and pentaprismane),and (iii) one truncated tetrahedrane (octahedrane). Our best theoretical heat of formation for cubane (144.8 kcal mol-1) suggests that the experimental value adopted by the NIST thermochemical database (142.7 ± 1.2 kcal mol-1) should be revised upwards by ∼2 kcal mol-1. Our best heat of formation for dodecahedrane (20.2 kcal mol-1) suggests that the semiexperimental value (22.4 ± 1 kcal mol-1) should be revised downward by ∼2 kcal mol-1. We use our benchmark Wn-F12TAEs to evaluate the performance of a variety of computation-ally less demanding composite thermochemical procedures. These include the Gaussian-n (Gn) and the complete basis set (CBS) methods. The CBS-QB3 and CBS-APNO procedures show relatively poor performance with root-mean-squared deviations (RMSDs) of 4.2 and 2.5 kcal mol-1, respectively. The best performers of the Gn procedures are G4 and G3(MP2)B3 (RMSD = 0.5 and 0.6 kcal mol-1, respectively), while the worst performers are G3 and G4(MP2)-6X (RMSD = 2.1 and 2.9 kcalmol-1, respectively). Isodesmic and even homodesmotic reactions involving these species are surprisingly challenging targets for DFT computations