### Abstract

Formulas for evaluating analytic energy gradient are derived for combined time-dependent density functional theory (TDDFT) and polarizable force field methods that incorporate dipole polarizability tensors and linearly induced point dipoles. The Z -vector method for determining relaxed one-particle difference density matrix in regular TDDFT methods is extended to include induced dipoles. The analytic gradient of the mutual polarization energy of the force field and the TDDFT excited state can be formulated by using the TDDFT difference density-induced dipoles and the transition state density-induced dipoles. All the forces and torques involving induced dipoles can be efficiently evaluated using standard electrostatic formulas as if the induced dipoles were permanent dipoles. The formulas are given in the most general form and are applicable to various flavors of polarizable force fields. Implementation and tests with a polarizable five-point water model show that the formulas are rigorous. The carbonyl vibration modes and infrared spectrum intensities of a cluster formed by acetone and two water molecules are studied.

Original language | English (US) |
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Article number | 144112 |

Journal | Journal of Chemical Physics |

Volume | 133 |

Issue number | 14 |

DOIs | |

State | Published - Oct 14 2010 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**Analytic energy gradient in combined time-dependent density functional theory and polarizable force field calculation.** / Si, Dejun; Li, Hui.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Analytic energy gradient in combined time-dependent density functional theory and polarizable force field calculation

AU - Si, Dejun

AU - Li, Hui

PY - 2010/10/14

Y1 - 2010/10/14

N2 - Formulas for evaluating analytic energy gradient are derived for combined time-dependent density functional theory (TDDFT) and polarizable force field methods that incorporate dipole polarizability tensors and linearly induced point dipoles. The Z -vector method for determining relaxed one-particle difference density matrix in regular TDDFT methods is extended to include induced dipoles. The analytic gradient of the mutual polarization energy of the force field and the TDDFT excited state can be formulated by using the TDDFT difference density-induced dipoles and the transition state density-induced dipoles. All the forces and torques involving induced dipoles can be efficiently evaluated using standard electrostatic formulas as if the induced dipoles were permanent dipoles. The formulas are given in the most general form and are applicable to various flavors of polarizable force fields. Implementation and tests with a polarizable five-point water model show that the formulas are rigorous. The carbonyl vibration modes and infrared spectrum intensities of a cluster formed by acetone and two water molecules are studied.

AB - Formulas for evaluating analytic energy gradient are derived for combined time-dependent density functional theory (TDDFT) and polarizable force field methods that incorporate dipole polarizability tensors and linearly induced point dipoles. The Z -vector method for determining relaxed one-particle difference density matrix in regular TDDFT methods is extended to include induced dipoles. The analytic gradient of the mutual polarization energy of the force field and the TDDFT excited state can be formulated by using the TDDFT difference density-induced dipoles and the transition state density-induced dipoles. All the forces and torques involving induced dipoles can be efficiently evaluated using standard electrostatic formulas as if the induced dipoles were permanent dipoles. The formulas are given in the most general form and are applicable to various flavors of polarizable force fields. Implementation and tests with a polarizable five-point water model show that the formulas are rigorous. The carbonyl vibration modes and infrared spectrum intensities of a cluster formed by acetone and two water molecules are studied.

UR - http://www.scopus.com/inward/record.url?scp=77958110649&partnerID=8YFLogxK

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U2 - 10.1063/1.3491814

DO - 10.1063/1.3491814

M3 - Article

C2 - 20949992

AN - SCOPUS:77958110649

VL - 133

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 14

M1 - 144112

ER -