^{1,a)}

### Abstract

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. The results for , , and demonstrate this method to be accurate for both geometries and energies. A comparison with density functional theory(DFT) and second-order Moller–Plesset (MP2) level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.

It is a pleasure to acknowledge Professor Neil Kester for useful discussions. The GAUSSIAN 98 calculations were performed by Cheri McFerrin. This work was partially supported by NSF Grant No. CHE 9977124 and by the Center for Computation and Technology at LSU.

I. INTRODUCTION

II. KINK-BASED PATH INTEGRAL FORMULATION

III. MONTE CARLO SAMPLING PROCEDURE

A. Rotations of single-particle states

B. Addition/removal of kinks

C. Moving atoms

IV. SIMULATION DETAILS

V. RESULTS AND DISCUSSION

VI. CONCLUSION

### Key Topics

- Excited states
- 32.0
- Light emitting diodes
- 27.0
- Ab initio calculations
- 16.0
- Ground states
- 12.0
- Monte Carlo methods
- 9.0

## Figures

Energies during different Monte Carlo simulations of . Energy during simulation is the energy during a simulation using Eq. (43), Hartree–Fock energy during simulation is the energy of the lowest-energy state during a simulation using Eq. (43), and energy during simulation is the energy during a simulation using Eq. (13).

Energies during different Monte Carlo simulations of . Energy during simulation is the energy during a simulation using Eq. (43), Hartree–Fock energy during simulation is the energy of the lowest-energy state during a simulation using Eq. (43), and energy during simulation is the energy during a simulation using Eq. (13).

Internuclear distances during different Monte Carlo simulations of using . The two hydrogen atoms are labeled and . The initial values of the interatomic distances correspond to the initial linear geometry.

Internuclear distances during different Monte Carlo simulations of using . The two hydrogen atoms are labeled and . The initial values of the interatomic distances correspond to the initial linear geometry.

## Tables

Energies, average number of excited states included in the path integral calculation , and structural parameters for . All energies and distances are in atomic units and numbers in parentheses represent two standard deviations (95% confidence limits). is the energy, including correlation, is the energy of the lowest energy state, is the average H–H bond length, is the average O–H bond length, and is the average H–O–H angle. Path integral calculations were performed at . *Ab initio* results were obtained using GAUSSIAN 98 (Ref. 27) and are given with and without the zero-point energy (ZPE) correction.

Energies, average number of excited states included in the path integral calculation , and structural parameters for . All energies and distances are in atomic units and numbers in parentheses represent two standard deviations (95% confidence limits). is the energy, including correlation, is the energy of the lowest energy state, is the average H–H bond length, is the average O–H bond length, and is the average H–O–H angle. Path integral calculations were performed at . *Ab initio* results were obtained using GAUSSIAN 98 (Ref. 27) and are given with and without the zero-point energy (ZPE) correction.

Energies, average number of excited states included in the path integral calculation , and structural parameters for . All energies and distances are in atomic units and numbers in parentheses represent two standard deviations (95% confidence limits). is the energy, including correlation, is the energy of the lowest energy state, is the average H–H bond length, is the average N–H bond length, and is the average H–N–H angle. Path integral calculations were performed at except as noted. *Ab initio* results were obtained using GAUSSIAN 98 (Ref. 27) and are given with and without the zero-point energy (ZPE) correction.

Energies, average number of excited states included in the path integral calculation , and structural parameters for . All energies and distances are in atomic units and numbers in parentheses represent two standard deviations (95% confidence limits). is the energy, including correlation, is the energy of the lowest energy state, is the average H–H bond length, is the average N–H bond length, and is the average H–N–H angle. Path integral calculations were performed at except as noted. *Ab initio* results were obtained using GAUSSIAN 98 (Ref. 27) and are given with and without the zero-point energy (ZPE) correction.

Energies, average number of excited states included in the path integral calculation , and structural parameters for . All energies and distances are in atomic units and numbers in parentheses represent two standard deviations (95% confidence limits). is the energy, including correlation, is the energy of the lowest energy state, is the average H–H bond length, is the average C–H bond length, and is the average H–C–H angle. Path integral calculations were performed at . *Ab initio* results were obtained using GAUSSIAN 98 (Ref. 27) and are given with and without the zero-point energy (ZPE) correction.

Energies, average number of excited states included in the path integral calculation , and structural parameters for . All energies and distances are in atomic units and numbers in parentheses represent two standard deviations (95% confidence limits). is the energy, including correlation, is the energy of the lowest energy state, is the average H–H bond length, is the average C–H bond length, and is the average H–C–H angle. Path integral calculations were performed at . *Ab initio* results were obtained using GAUSSIAN 98 (Ref. 27) and are given with and without the zero-point energy (ZPE) correction.

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