# Your search: "author:Head-Gordon, Martin"

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## Scholarly Works (255 results)

The work herein is concerned with developing computational models to understand molecules. The underlying theme of this research is the reassessment of zeroth-order approximations for higher-level methods. For second-order Moller-Plesset theory (MP2), qualitative failures of the Hartree-Fock orbitals in the form of spin contamination can lead to catastrophic errors in the second order energies. By working with orbitals optimized in the presence of correlations, orbital-optimized MP2 can fix the spin contamination problem that plague radicals, aromatics, and transition metal complexes. In path integral Monte Carlo for vibrational energies, the zeroth-order propagator is typically chosen to be the most general possible, the free particle propagator; we chose to be informed by the molecular structure we have already attained and apply a propagator based on the harmonic modes of the molecule, improving sampling efficiency and our Trotter approximation.

This thesis describes several new theoretical developments that facilitate

the computation of the exact exchange energy, a vital component of accurate

molecular simulations. The primary technique on which these

developments are based is the resolution of the identity approximation,

particularly the pair atomic resolution of the identity approximation (PARI).

We prove that computation of exact exchange using the PARI approximation

is variationally stable, and provide benchmarks of the performance and accuracy

of our implementation. We then show that the most commonly used SCF convergence acceleration algorithm, DIIS,

enables the design of a new fast exchange algorithm that we designate as occ-RI-K.

Next, we combine the preceding occ-RI-K algorithm with the PARI approximation

to create a linear-scaling

exact exchange algorithm for the specific case of large weakly-interacting systems.

Finally, we discuss our development of a high-level, object-oriented software library for

block-sparse tensor operations. This library provides the underlying implementation

for all of the algorithms discussed in this thesis.

_{3}CH···Y (Y = H

_{2}O, NH

_{3}, Cl

^{-}) complexes. We reveal that features of a blue-shifting H-bond already appear on the frozen surface where both polarization and charge transfer (CT) are "turned off", and that the final frequency shift observed depends on the strength of CT. Further decomposition of forces at the frozen level shows that Pauli repulsion is the only component that shortens the C-H bond in the short-range, while both permanent electrostatics and dispersion lengthen the bond. The effects of these forces from the medium to long-range are also discussed. Our analysis provides a complete picture for blue-shifting H-bonds and suggests two necessary conditions for their features to be observed at equilibrium structures: (i) stronger Pauli repulsion than the combination of electrostatic and dispersion forces; (ii) relatively weak CT that is insufficient to compensate for the blue-shifting effect of the frozen interaction.

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