# Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space

## Abstract

Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present paper revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does notmore »

- Authors:

- Queens College (CUNY), NY (United States). Dept. of Chemistry and Biochemistry; City Univ. of New York (CUNY), NY (United States). Graduate Center. Ph.D Programs in Chemistry and Physics. Initiative for the Theoretical Sciences
- Univ. of Chicago, IL (United States). Dept. of Chemistry. James Franck Inst. Inst. for Biophysical Dynamics

- Publication Date:

- Research Org.:
- Queens College (CUNY), NY (United States); City Univ. of New York (CUNY), NY (United States); Univ. of Chicago, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)

- OSTI Identifier:
- 1465983

- Alternate Identifier(s):
- OSTI ID: 1361846

- Grant/Contract Number:
- SC0001393; CHE-1362926; CHE-1465248

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 146; Journal Issue: 17; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; polymers; carbon dioxide; classical mechanics; correlation functions; molecular dynamics; quantum fluctuations; transition state theory; surface dynamics; classical ensemble theory; quantum measurement theory

### Citation Formats

```
Jang, Seogjoo, and Voth, Gregory A.
```*Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space*. United States: N. p., 2017.
Web. doi:10.1063/1.4982053.

```
Jang, Seogjoo, & Voth, Gregory A.
```*Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space*. United States. doi:10.1063/1.4982053.

```
Jang, Seogjoo, and Voth, Gregory A. Tue .
"Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space". United States.
doi:10.1063/1.4982053. https://www.osti.gov/servlets/purl/1465983.
```

```
@article{osti_1465983,
```

title = {Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space},

author = {Jang, Seogjoo and Voth, Gregory A.},

abstractNote = {Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present paper revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Finally, our analysis also offers new insights into similar path integral based QTST approaches.},

doi = {10.1063/1.4982053},

journal = {Journal of Chemical Physics},

number = 17,

volume = 146,

place = {United States},

year = {Tue May 02 00:00:00 EDT 2017},

month = {Tue May 02 00:00:00 EDT 2017}

}

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