^{1}, Michael V. Pak

^{1}and Sharon Hammes-Schiffer

^{1,a)}

### Abstract

This paper addresses fundamental issues that arise in the application of the nuclear-electronic orbital (NEO) approach to systems with equivalent quantum nuclei. Our analysis illustrates that Hartree-Fock nuclear wave functions do not provide physically reasonable descriptions of systems comprised of equivalent low-spin fermions or equivalent bosons. The physical basis for this breakdown is that the ionic terms dominate due to the localized nature of the nuclear orbitals. Multiconfigurational wave functions that include only covalent terms provide physically reasonable descriptions of these types of systems. The application of the NEO approach to a variety of chemical systems is presented to elucidate the isotope effects on the geometries and electronic wave functions. Deuteration of hydrogen halides, water, ammonia, and hydronium ion decreases the bond length and the magnitude of negative partial atomic charge on the heavy atom. These results are consistent with experimental spectroscopic data. Deuteration at the beta position for formate anion and a series of amines increases the magnitude of negative partial atomic charge on the protonation site for the unprotonated species. This observation is consistent with the experimentally observed increase in basicity upon deuteration at the beta position for carboxylic acids and amines.

We gratefully acknowledge the support of AFOSR Grant No. F49620-01-1-0046 and NIH Grant GM56207 and helpful discussions with Chet Swalina and Simon Webb.

I. INTRODUCTION

II. THEORY

III. APPLICATIONS

IV. CONCLUSIONS

### Key Topics

- Wave functions
- 51.0
- Kinetic isotope effects
- 29.0
- Hydrogen bonding
- 17.0
- Chemical bonds
- 16.0
- Fermion systems
- 14.0

## Figures

Schematic picture of the water dimer (top) and the ammonia-water dimer (bottom), where the hydrogen nuclei are treated quantum mechanically. The oxygen atoms are dark gray, and the nitrogen atom is light gray. The quantum nuclei are represented by nuclear orbitals.

Schematic picture of the water dimer (top) and the ammonia-water dimer (bottom), where the hydrogen nuclei are treated quantum mechanically. The oxygen atoms are dark gray, and the nitrogen atom is light gray. The quantum nuclei are represented by nuclear orbitals.

Schematic picture of the formate anion, where the hydrogen nucleus is treated quantum mechanically. The carbon atom is black, and the oxygen atoms are gray. The quantum nucleus is represented by a nuclear orbital.

Schematic picture of the formate anion, where the hydrogen nucleus is treated quantum mechanically. The carbon atom is black, and the oxygen atoms are gray. The quantum nucleus is represented by a nuclear orbital.

Schematic picture of methylamine (top), dimethylamine (middle), and trimethylamine (bottom), where the methyl group hydrogen nuclei are treated quantum mechanically. The carbon atoms are black, and the nitrogen atoms are gray. The quantum nuclei are represented by nuclear orbitals.

Schematic picture of methylamine (top), dimethylamine (middle), and trimethylamine (bottom), where the methyl group hydrogen nuclei are treated quantum mechanically. The carbon atoms are black, and the nitrogen atoms are gray. The quantum nuclei are represented by nuclear orbitals.

## Tables

Values of the integrals and energies for a system of two fermions with mass of and a system of two bosons with mass of All energies are given in a.u.

Values of the integrals and energies for a system of two fermions with mass of and a system of two bosons with mass of All energies are given in a.u.

Exponents in the DZSPDN nuclear basis sets optimized for H, D, and T.

Exponents in the DZSPDN nuclear basis sets optimized for H, D, and T.

Expectation value of the bond length and the partial atomic charge on the heavy atom for a series of small molecules calculated with the NEO approach. The partial atomic charges are calculated with the Mulliken, CHELPG, and Merz-Kollman (MK) methods. The expectation values are given in angstroms.

Expectation value of the bond length and the partial atomic charge on the heavy atom for a series of small molecules calculated with the NEO approach. The partial atomic charges are calculated with the Mulliken, CHELPG, and Merz-Kollman (MK) methods. The expectation values are given in angstroms.

Geometric parameters for the water dimer and the ammonia-water dimer optimized with the NEO approach. In the notation for the distances, the subscripts D, A, and Y correspond to the hydrogen bond donor, the hydrogen bond acceptor, and the intervening light atom (H, D, or T). The molecules are depicted in Fig. 1. The distances are given in angstroms.

Geometric parameters for the water dimer and the ammonia-water dimer optimized with the NEO approach. In the notation for the distances, the subscripts D, A, and Y correspond to the hydrogen bond donor, the hydrogen bond acceptor, and the intervening light atom (H, D, or T). The molecules are depicted in Fig. 1. The distances are given in angstroms.

Expectation values of the bond lengths and the partial atomic charges on the oxygen of the formate anion calculated with the NEO approach. The partial atomic charges are calculated with the Mulliken, CHELPG, and Merz-Kollman (MK) methods. The molecule is depicted in Fig. 2. The expectation values are given in angstroms.

Expectation values of the bond lengths and the partial atomic charges on the oxygen of the formate anion calculated with the NEO approach. The partial atomic charges are calculated with the Mulliken, CHELPG, and Merz-Kollman (MK) methods. The molecule is depicted in Fig. 2. The expectation values are given in angstroms.

Expectation values of the bond lengths and the partial atomic charges on the nitrogen of methylamine, dimethylamine, and trimethylamine calculated with the NEO approach. Note that two different values of are given for the two distinct orientations of light atoms in the methyl groups. The partial atomic charges are calculated with the Mulliken, CHELPG, and MK methods. The molecules are depicted in Fig. 3. The expectation values are given in angstroms.

Expectation values of the bond lengths and the partial atomic charges on the nitrogen of methylamine, dimethylamine, and trimethylamine calculated with the NEO approach. Note that two different values of are given for the two distinct orientations of light atoms in the methyl groups. The partial atomic charges are calculated with the Mulliken, CHELPG, and MK methods. The molecules are depicted in Fig. 3. The expectation values are given in angstroms.

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