# Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities

## Abstract

We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.

- Authors:

- Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan)
- Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur (Belgium)

- Publication Date:

- OSTI Identifier:
- 22390901

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1642; Journal Issue: 1; Conference: ICCMSE-2010: International Conference of Computational Methods in Sciences and Engineering 2010, Kos (Greece), 3-8 Oct 2010; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; DENSITY FUNCTIONAL METHOD; ELECTRONS; PERFORMANCE; POLARIZABILITY; SPIN; SYMMETRY BREAKING; VARIATIONS

### Citation Formats

```
Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Champagne, Benoît, and Botek, Edith.
```*Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities*. United States: N. p., 2015.
Web. doi:10.1063/1.4906627.

```
Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Champagne, Benoît, & Botek, Edith.
```*Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities*. United States. doi:10.1063/1.4906627.

```
Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp, Champagne, Benoît, and Botek, Edith. Thu .
"Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities". United States.
doi:10.1063/1.4906627.
```

```
@article{osti_22390901,
```

title = {Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities},

author = {Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp and Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp and Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp and Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp and Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp and Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp and Champagne, Benoît and Botek, Edith},

abstractNote = {We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.},

doi = {10.1063/1.4906627},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1642,

place = {United States},

year = {Thu Jan 22 00:00:00 EST 2015},

month = {Thu Jan 22 00:00:00 EST 2015}

}