Franck–Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free, numerically stable derivation
Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests o...
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| Veröffentlicht in: | The Journal of chemical physics 2022-09, Vol.157 (12), p.124102-124102 |
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| container_end_page | 124102 |
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| container_issue | 12 |
| container_start_page | 124102 |
| container_title | The Journal of chemical physics |
| container_volume | 157 |
| creator | Changala, P. Bryan Genossar, Nadav Baraban, Joshua H. |
| description | Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulas. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck–Condon approximation for the lowest-order anharmonic and Herzberg–Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2. |
| doi_str_mv | 10.1063/5.0112217 |
| format | Article |
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Bryan ; Genossar, Nadav ; Baraban, Joshua H.</creator><creatorcontrib>Changala, P. Bryan ; Genossar, Nadav ; Baraban, Joshua H.</creatorcontrib><description>Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulas. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck–Condon approximation for the lowest-order anharmonic and Herzberg–Teller effects. 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Simple extensions correct the harmonic Franck–Condon approximation for the lowest-order anharmonic and Herzberg–Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2.</description><subject>Absorption spectra</subject><subject>Anharmonicity</subject><subject>Arithmetic</subject><subject>Autocorrelation functions</subject><subject>Derivation</subject><subject>Electronic spectra</subject><subject>Harmonic functions</subject><subject>Lie groups</subject><subject>Mathematical analysis</subject><subject>Nitrogen dioxide</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Wave packets</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kb1O5DAQgC0EEstPwRtYouHQBcZ2bCfXoRXcnYREA3U0cWwIZO09O0HajldAvCFPgtmluoJiNKOZb_4JOWJwxkCJc3kGjHHO9BaZMajqQqsatskMgLOiVqB2yV5KjwDANC9n5PUqojdP7y9v8-C74GlaWjNGpMHRybdh8h3FLP0C73uPcVW4aP9N1psVfe7biGMffMomUhNitMPaQd3kzTryi17Q9rPFQ2GmkeZk-5P6aWFjb3AYVjSN2A6WdtnxvM49IDsOh2QPv_Q-ubu6vJ3_Ka5vfv-dX1wXRnA5FoY5kEq0SjHXcYklqyrFnUDNTFkKK7koZSsqpkEL4ZDrri2VrFGJGrGuxT452dRdxpAXSmOz6JOxw4Dehik1XHMoeQ1cZfT4P_QxTNHn6TLFlAbJRJWpHxvKxJBStK5Zxny2uGoYNJ_PaWTz9ZzMnm7YZPpxvfY38Ae1CpCF</recordid><startdate>20220928</startdate><enddate>20220928</enddate><creator>Changala, P. 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| ispartof | The Journal of chemical physics, 2022-09, Vol.157 (12), p.124102-124102 |
| issn | 0021-9606 1089-7690 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_5_0112217 |
| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Absorption spectra Anharmonicity Arithmetic Autocorrelation functions Derivation Electronic spectra Harmonic functions Lie groups Mathematical analysis Nitrogen dioxide Operators (mathematics) Physics Wave packets |
| title | Franck–Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free, numerically stable derivation |
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