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University of Texas – Austin

1. -6705-8755. From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules.

Degree: PhD, Chemistry, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/47232

The first section of this work details a force field modeled on VSEPR theory. Previous studies¹ from Bartell et al. have validated the use of the following function to describe repulsion between outer atoms, X [subscript i], bonded to a shared center, A, in binary compounds of the form AX [subscript n]: V=K/r [superscript n above subscript ij]. Here, K and n are parameters and r [subscript ij] is the distance between repelled atoms. Bartell et al. fixed the bond distances A-X [subscript i] so that the atoms X [subscript i] are “points-on-a-sphere” around the central atom A. Our current work extends this POS force field to include flexibility in the bond distances A-X [subscript i]. The functional form for the energy of the bonds is that of the Morse oscillator: V [subscript m, sub-subscript i] = D [subscript e](1 – exp[ – α(r [subscript i] – Re)])². Here, D [subscript e], α, and R [subscript e] are parameters of the force field and r [subscript i] is the distance between atoms A and X [subscript i]. This extended VSEPR force field is applied to PF₅. Parameters were optimized to minimize differences between the VSEPR and MP2/cc-pVTZ PF₅ diagonal quadratic force constants. Quadratic and cubic bending and stretching force constants are presented and compared between Morse-POS and MP2/cc-pVTZ methods. The second section of this dissertation focuses on the analytical transformation of force constants and molecular properties between isotopologues. Within the Born-Oppenheimer approximation, potential energy surfaces of isotopologues are identical. When beginning an exploration of a Born-Oppenheimer potential energy surface, a molecular geometry is chosen and the energy and derivatives are calculated. The most efficient choice of coordinates for these derivatives is normal coordinates, which are mass dependent. This thesis details the transformation of force constants, dipole moments, derivatives of dipole moments, rotational constants, and Coriolis constants from one isotopologue to another. Two alternative systems of coordinates for use in quantum chemical calculations are rectilinear and curvilinear internal coordinates. Rectilinear internal coordinates express the displacement of atoms in a molecule as changes in bond length, bond angle, and dihedral angle as linear combinations of Cartesian coordinates. Though other internal coordinates exist, the previously mentioned are the most commonly used. There are immediate problems with the general use of rectilinear internal coordinates. When one calculates the displacement in Cartesian coordinates needed to increase a bond angle, the bond angle does not scale linearly with the Cartesian coordinates. The following thesis provides the derivation of equations that allow for the analytical transformation from rectilinear to curvilinear coordinates of first through fourth derivatives of the energy. As shown here, these transformations may also be used in converting between the force fields of isotopologues. Additionally, the transformations used between force fields of…
*Advisors/Committee Members: Stanton, John (John F.) (advisor), Ellison, Barney (committee member), Anslyn, Eric (committee member), Makarov, Dmitrii (committee member), Henkelman, Graeme (committee member).*

Subjects/Keywords: Ab initio; VSEPR; Phosphorus pentafluoride; Force field; Isotopomer; VPT2; Dihydroxycarbene

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APA (6^{th} Edition):

-6705-8755. (2016). From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/47232

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Chicago Manual of Style (16^{th} Edition):

-6705-8755. “From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed October 18, 2019. http://hdl.handle.net/2152/47232.

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Author name may be incomplete

MLA Handbook (7^{th} Edition):

-6705-8755. “From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules.” 2016. Web. 18 Oct 2019.

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Author name may be incomplete

Vancouver:

-6705-8755. From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2019 Oct 18]. Available from: http://hdl.handle.net/2152/47232.

Author name may be incomplete

Council of Science Editors:

-6705-8755. From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/47232

Author name may be incomplete