Sains Malaysiana 41(4)(2012): 445-452

Effects of Spin Contamination on the Stability and Spin Density of Wavefunction of  Graphene: Comparison between First Principle and Density Functional Methods

(Kesan Pelumusan Spin Terhadap Kestabilan dan Ketumpatan Spin bagi Fungsi  Gelombang Grafen pelumusan: Perbandingan antara Kaedah Prinsip Pertama  dan Kaedah Kefungsian Ketumpatan)

Lee Sin Ang* & Shukri Sulaiman

Physical Sciences Programme, School of Distance Education

Universiti Sains Malaysia, 11800 Penang, Malaysia

Mohamed Ismail Mohamed-Ibrahim

Chemical Sciences Programme, School of Distance Education

Universiti Sains Malaysia, 11800 Penang, Malaysia

Received: 13 May 2011 / Accepted: 7 October 2011

ABSTRACT

The effects of spin contamination on the stability and the spin densities of a model of graphene in the Hartree-Fock wavefunction (HF), Møller-Plesset perturbation theory (second order, MP2 and fourth order, MP4) and density functional theory (B3LYP and PBEPBE) are reported. It was found that the Hartree-Fock and MP2 wavefunctions of graphene suffer from the contamination from higher spin states and spin projection method failed to project out the spin contaminants. The spin density from HF was overestimated, while for MP2 it has the wrong trend. B3LYP and PBEPBE wave functions however have negligible contamination for higher spin states. Comparison with reported results showed that the spin

densities at the center of the molecule from the pure functionals of PBEPBE were underestimated. Based on the comparison made, it was concluded that among the methods considered, the suitable one for use in the calculations of pristine graphene was B3LYP.

Keywords: Density functional theory; grapheme; Hartree-Fock; Møller-Plesset perturbation theory; spin

contamination

ABSTRAK

Kesan pelumusan spin ke atas kestabilan dan ketumpatan spin di dalam fungsi gelombang Hartree-Fock (HF), teori gangguan Møller-Plesset (tertib kedua, MP2 dan tertib keempat, MP4) dan teori fungsi ketumpatan (B3LYP dan PBEPBE) bagi model grafen dilaporkan. Didapati bahawa fungsi gelombang HF dan MP2 bagi grafen mengalami pelumusan daripada keadaan spin lebih tinggi dan kaedah projeksi gagal mengeluarkan pelumusan putaran. Nilai ketumpatan spin daripada HF adalah terlebih anggar, manakala untuk MP2 ia mempunyai corak yang salah. B3LYP dan PBEPBE mempunyai pelumusan spin yang boleh diabaikan. Perbandingan dengan keputusan yang telah dilaporkan menunjukkan bahawa ketumpatan spin pada bahagian tengah molekul daripada kefungsian tulen PBEPBE adalah terkurang anggar. Berdasarkan perbandingan yang dilakukan, disimpulkan bahawa antara kaedah-kaedah yang dipertimbangkan, B3LYP merupakan kaedah yang sesuai untuk pengiraan melibatkan grafen tulen.

Kata kunci: Grafin; Hartree-Fock; pencemaran putaran; teori gangguan Møller-Plesset; teori fungsi ketumpatan

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*Corresponding author; email: lsina2002@hotmail.com