Fast and Accurate Computation of Nonadiabatic Coupling Matrix Elements Using the Truncated Leibniz Formula and Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory
Abstract
We present a fast and accurate numerical algorithm for computing the first-order nonadiabatic coupling matrix element (NACME). The algorithm employs the truncated Leibniz formula (TLF) approximation within the finite-difference method, which makes it easily applicable in connection with any wave function-based methodology. In this work, we used the algorithm in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT, MRSF for brevity). The accuracy is assessed for NACME between the singlet electronic states of a dissociating hydrogen molecule. It is demonstrated that an intermediate approximation, TLF(1), affords a negligible numeric error on the order of ∼10⁻¹⁰ a.u. while enabling a fast computation of NACME. As the MRSF method yields the correct description of the dissociation curves of H₂ for all the electronic states involved, the numeric TLF(1)/MRSF NACME values are in excellent agreement with the reference analytical values obtained by the full configuration interaction. For polyatomic molecules, the MRSF NAC vectors agree very closely with the MRCISD NAC vectors. Hence, the proposed protocol is a promising tool for the evaluation of NACMEs.
Additional Information
© 2021 American Chemical Society. Received: March 23, 2021; Accepted: May 7, 2021; Published: May 13, 2021. This work was supported by the Samsung Science and Technology Foundations Grant SSTF-BA1701-12 (to C.H.C.) for fundamental theory developments and the NRF grants 2019H1D3A2A02102948 (to M.F.) and 2020R1A2C2008246 and 2020R1A5A1019141 (to C.H.C.) funded by the Ministry of Science and ICT for applications of the developed methodologies. S.L. was supported by the US National Science Foundation via Award CHE-1655333. The authors declare no competing financial interest.Attached Files
Supplemental Material - jz1c00932_si_001.pdf
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Additional details
- Eprint ID
- 109124
- DOI
- 10.1021/acs.jpclett.1c00932
- Resolver ID
- CaltechAUTHORS:20210513-144618100
- SSTF-BA1701-12
- Samsung Science and Technology Foundation
- 2019H1D3A2A02102948
- National Research Foundation of Korea
- 2020R1A2C2008246
- National Research Foundation of Korea
- 2020R1A5A1019141
- National Research Foundation of Korea
- CHE-1655333
- NSF
- Created
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2021-05-14Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field