### Abstract

A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (β) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal β of four typical push-pull π-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for β and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the "exact" correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull π-conjugated systems to estimate the static β, and the error in the value so obtained, by averaging the Kuzyk and traditional results.

Original language | English |
---|---|

Article number | 024101 |

Journal | The journal of chemical physics |

Volume | 125 |

Issue number | 2 |

DOIs | |

Publication status | Published - 26 Jul 2006 |

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*The journal of chemical physics*, vol. 125, no. 2, 024101. https://doi.org/10.1063/1.2206181

**Evaluation of alternative sum-over-states expressions for the first hyperpolarizability of push-pull π-conjugated systems.** / Champagne, Benoît; Kirtman, Bernard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Evaluation of alternative sum-over-states expressions for the first hyperpolarizability of push-pull π-conjugated systems

AU - Champagne, Benoît

AU - Kirtman, Bernard

PY - 2006/7/26

Y1 - 2006/7/26

N2 - A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (β) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal β of four typical push-pull π-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for β and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the "exact" correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull π-conjugated systems to estimate the static β, and the error in the value so obtained, by averaging the Kuzyk and traditional results.

AB - A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (β) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal β of four typical push-pull π-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for β and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the "exact" correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull π-conjugated systems to estimate the static β, and the error in the value so obtained, by averaging the Kuzyk and traditional results.

UR - http://www.scopus.com/inward/record.url?scp=33746217377&partnerID=8YFLogxK

U2 - 10.1063/1.2206181

DO - 10.1063/1.2206181

M3 - Article

VL - 125

JO - The journal of chemical physics

JF - The journal of chemical physics

SN - 0021-9606

IS - 2

M1 - 024101

ER -