GW Calculation of a Carbon Oxide Molecule Using an All-Electron Mixed-Basis Approach Soh Ishii 1 , Kaoru Ohno 2 and Yoshiyuki Kawazoe 1 1 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 2 Department of Physics, Graduate school of Engineering, Yokohama National University, Yokohama 240-8501, Japan An ab-initio calculation for a carbon oxide molecule using the Green’s function approach within the GW approximation was performed. We use an all-electron mixed-basis approach, where one wave function is expanded using both plane waves and atomic orbitals. This approach has an advantage to describe the wave function of a carbon and oxide, compared with a pseudopotential approach requiring higher cutoff energy. Obtaied GW quasiparticle energies are in good agreement with avairable experimental value and previous GW calculation. (Received December 24, 2003; Accepted February 20, 2004) Keywords: GW approximation, carbon oxide, first-principles, electron correlation, ionization potential, electron affinity 1. Introduction The carbon oxide molecule is important from the view- point of not only engieering side but also physical side and has been widely investigated both experimentally and theoretically. In the investigation of such small molecules, ionization potentials (IPs) and electron affinities (EAs) are important because these quantities, for example, play an significant role to deteremine chemical reactions and optical properties. To evaluate IPs and EAs by means of ab-initio calculations, there are at least two methods. The first method is taking total energy difference between a cation (anion) and neutral molecules for evaluating the IP (EA). However, one needs calculate total energy at least three times to obtain both IP and EA. The second is using the Koopmans theorem: the absolute value of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy is the IP and EA, respectively. The approach using this theorem is significantly different from the first one. This method has an advantage from the viewpoint of the times of calculations:this method simultaneously gives all the energy levels (for example, one can get the IP and EA at the same time). In ab-initio calculations, one of the standard methods is the local density approximation (LDA) 1) within the density functional theory (DFT), 2) which is a very good theory for the description of the ground state properties. However, ionization potentials (electron affinities) of the LDA via Koopmans theorem underestimates (overestimates) experimental IPs (EAs) very much. Note that the absolute value of the HOMO energy is identical to IP even within the density functional theory. 3) In the present study, we take the latter approach and employ the Green’s function approach within the GW approximation, 4) which gives the one-particle excitation energy correctly. In the GW approximation, electron self- energy operator is defined by using one-particle Green’s function and dynamically screened Coulomb interaction. Historically, ab-initio GW calculations were firstly per- formed by Hybertsen and Louie 5) for typical semiconductors such as silicon and germanium successfully. However, the number of papers of the GW calculations for isolated systems such as molecules and clusters are small. 6–12) In addition, almost all calculations employ a pseudopotential approach. We successfully applied ab-initio GW calculations to small alkali-metal clusters 9,10) and silicon clusters, 11) using an all- electron mixed-basis approach. In the present paper, we perform an ab-initio GW calculation for a carbon oxide molecule using an all-electron mixed-basis approach and compare with other calcula- tioins 12) and experimental data. In the next section, we explain our method briefly. Sec. 3 is devoted to the results and discussion. Sec. 4 is summary. 2. Methodology We employ an all-electron mixed-basis approach, where a wave function is expanded using both plane waves and atomic orbitals, where the one-particle wave function is represented by plane waves (PWs) and atomic orbitals (AOs) to take into account both the core electron states and the empty free-electron-like states accurately. This approach has been successfully applied not only to isolated systems but also to infinite systems. 9,13,14) This approach also has an advantage for the study of second row elements such as carbon, nitrogen, oxygen, and so on because the cut-off energy for the PWs needed in the present approach is much smaller than that of a pseudopotential approach (see below). As an atomic orbital, we employ Herman-Skillman code 15) to make atomic orbitals. In the GW approximation (GWA), the one-electron self- energy operator ðr; r 0 ; !Þ is given by (apart from the Hartree potential) 4) ðr; r 0 ; !Þ¼ i 2% Z Gðr; r 0 ; ! þ ! 0 ÞWðr; r 0 ; ! 0 Þe i! 0 d! 0 ; ð1Þ where G and W denote the one-particle Green’s function and the dynamically screened Coulomb interaction,respectively.  is a positive infinitesimal number. W is usually evaluated within the random phase approximation. The Fock exchange part of the self-energy,  x , is obtained by replacing W with the bare Coulomb interaction in eq. (1), while we call  c ¼    x the correlation part. Note that self-energy operator is Materials Transactions, Vol. 45, No. 5 (2004) pp. 1411 to 1413 Special Issue on Advances in Computational Materials Science and Engineering III #2004 The Japan Institute of Metals