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

Benoît Champagne, Bernard Kirtman

Research output: Contribution to journalArticle

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 languageEnglish
Article number024101
JournalThe journal of chemical physics
Volume125
Issue number2
DOIs
Publication statusPublished - 26 Jul 2006

Fingerprint

Excited states
Commonwealth of Independent States
evaluation
Tensors
excitation
tensors
estimates

Cite this

@article{7dc7e009aaaf4ae398aacca5156bdd82,
title = "Evaluation of alternative sum-over-states expressions for the first hyperpolarizability of push-pull π-conjugated systems",
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.",
author = "Beno{\^i}t Champagne and Bernard Kirtman",
year = "2006",
month = "7",
day = "26",
doi = "10.1063/1.2206181",
language = "English",
volume = "125",
journal = "The journal of chemical physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "2",

}

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

In: The journal of chemical physics, Vol. 125, No. 2, 024101, 26.07.2006.

Research output: Contribution to journalArticle

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 -