UNIVERSITY OF MALAYA UNIVERSITI MALAYA EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE PEPERIKSAAN IJAZAH SARJANA MUDA SAINS ACADEMIC SESSION 2011/2012 : SEMESTER 2 SESI AKADEMIK 2011/2012 : SEMESTER 2 SCES3337 : Computational Chemistry II Kimia Pengkomputeran II June 2012 Jun 2012 Time : 2 hours Masa : 2 jam INSTRUCTIONS TO CANDIDATES : ARAHAN KEPADA CALON This paper is divided into Section A, B and C. Kertas ini dibahagikan kepada Bahagian A, B dan C.. Please follow the instruction given in each section. Sila patuhi arahan yang diberikan dalam setiap bahagian semasa menjawab. (This question paper consists of 12 questions on 6 printed pages) (Kertas soalan ini mengandungi 12 soalan dalam 6 halaman yang dicetak)
SCES3337/02 SECTION/BAHAGIAN A (30 marks/markah) Answer ALL questions in this section. Jawab SEMUA soalan dalam bahagian ini. 1. There are generally 3 type of models used in computational chemistry, ab initio, semi-empirical and molecular mechanics. Describe these models, taking into consideration their comparative advantages and disadvantages and their suitability for different types of chemical problem. Secara umumnya terdpat 3 jenis model yang digunakan didalam kimia pengkomputan, ab initio, separa empirik dan mekanik molekul. Terangkan model-model ini dengan mengambil kira kebaikan dan keburukan komparatif serta kesesuaiannya untuk masalah kimia yang berbeza-beza. (16 marks/markah) 2. Write a short discussion on the zero differential overlap (ZDO)? Bincangkan dengan ringkas mengenai zero differential overlap (ZDO). (14 marks/markah) SECTION/BAHAGIAN A (30 marks/markah) Answer ALL questions in this section. Jawab SEMUA soalan dalam bahagian ini. 3. What is Kohn Sham calculation? Explain the idea of density function theory for hydrogen molecule? Apakah pengiraan Kohn Sham? Jelaskan mengenai idea teori fungsi ketumpatan untuk molekul hidrogen. (10 marks/markah) 4. Why is a Kohn Sham calculation much faster than a traditional wavefunction calculation? Mengapakah pengiraan Kohn-Sham adalah lebih cepat daripada pengiraan fungsi gelombang tradisional? (5 marks/markah)
SCES3337/03 5. Identify the possible potential (Exact, HF, LDA, GGA) in the following graph. Kenalpasti lengkungan keupayaan (Exact, HF, LDA, GGA) dalam graf berikut. (4 marks/markah) 6. What methods have been used to approximate exchange-correlation functional? Explain two different methods in detail. Kaedah apakah yang digunakan untuk membuat anggaran untuk korelasitukaran? Terangkan dua kaedah yang berbeza ini secara terperinci. (6 marks/markah) 7. A successful hybrid functional for exchange-correlation functional was introduced by Becke. Explain the exchange energy of this hybrid functional. Sebuah fungsional hibrid yang berjaya telah diperkenalkan oleh Becke. Jelaskan tenaga pertukaran bagi fungsi hibrid ini. (5 marks/markah)
SCES3337/04 SECTION/BAHAGIAN C (40 marks/markah) Answer ALL questions in this section. Jawab SEMUA soalan dalam bahagian ini. 8. Ab initio Hartree-Fock calculations are performed on the H, He and Li atoms, and on the isoelectronic He 2 and LiH molecules, giving the electronic kinetic energies (T e ), and the potential energies between electrons and nuclei (V Ne ), electrons and other electrons (V ee ), and nuclei and other nuclei (V NN ): (all energies are in atomic units, 1 a.u. = 2625 kj mole -1.) Pengiraan-pengiraan ab initio Hartree-Fock dijalankan keatas atom-atom H, He dan Li, dan molekul-molekul isoelektronik He 2 and LiH, menghasilkan tenagatenaga kinetic elektronik (T e ), dan tenaga-tenaga keupayaan di antara elektronelektron dan nucleus-nukleus (V Ne ), elektron-elektron dan lain-lain electron (V ee ), dan nukleus-nukleus dan lain-lain nukleus (V NN ): (kesemua tenaga adalah didalam unit atomik, 1 a.u. = 2625 kj mol -1.) Te VNe Vee VNN He 2.8599-6.7459 1.0262 0.0000 He2 6.3203-18.3003 4.1423 2.3519 H 0.4998-0.9996 0.0000 0.0000 Li 7.4322-17.1461 2.2819 0.0000 LiH 7.9785-20.4234 3.4721 0.9874 Calculate and discuss the bond energy of both molecules. Kirakan dan bincangkan tenaga pengikatan kedua-dua molekul. (10 marks/markah)
SCES3337/05 9. The following Gaussian 94 basis-set data gives the orbital exponents and contraction coefficients for the nitrogen atom: Data basis-set Gaussian 94 berikut memberikan eksponen-eksponen orbital dan koefisi-koefisi pengecutan untuk atom nitrogen: BASIS="6-31G*" N 0 S 6 1.00 4173.51100 0.183480000E-02 627.457900 0.139950000E-01 142.902100 0.685870000E-01 40.2343300 0.232241000 12.8202100 0.469070000 4.39043700 0.360455000 SP 3 1.00 11.6263580-0.114961000 0.675800000E-01 2.71628000-0.169118000 0.323907000 0.772218000 1.14585200 0.740895000 SP 1 1.00 0.212031300 1.00000000 1.00000000 D 1 1.00 0.800000000 1.00000000 Write explicitly the contracted Gaussian-type orbitals (CGTO) for the nitrogen atom using the above data. Choose only one p orbital and one d orbital out of three p orbitals and five d orbitals respectively. Tulis secara lengkap contracted Gaussian-type orbitals (CGTO) bagi atom nitrogen menggunakan data di atas. Pilih cuma satu orbital p dan satu orbital d daripada tiga orbital p dan lima orbital d masing-masing. (10 marks/markah) 10. For a configuration interaction (CI) calculation of the H 2 first excited electronic state, which of the following electron configurations will produce a CSF that will contribute to the wave function? (i) (1 g ) (2 g ); (ii) (1 g ) (3 u ); (iii) (1 u ) 2 ; (iv) (1 u )(1 g ); (v) (1 u ) (3 u ); (vi) (1 u ) 2 ; (vii) (1 u ) (2 u ). Explain. Untul satu pengiraan configuration interaction (CI) bagi keadaan pengujaan elektronik pertama H 2, yang mana daripada konfigurasi-konfigurasi elektron berikut yang akan menghasilkan satu CSF yang menyumbang kepada fungsi gelombangnya? (i) (1 g ) (2 g ); (ii) (1 g ) (3 u ); (iii) (1 u ) 2 ; (iv) (1 u )(1 g ); (v) (1 u ) (3 u ); (vi) (1 u ) 2 ; (vii) (1 u ) (2 u ). Terangkan. (6 marks/markah)
SCES3337/06 11. For a complete active space self-consistent-field (CASSCF) wave function in which the active orbitals are taken as those that arise from the 2s and 2p atomic orbitals, state the number of active electrons and the maximum number of electrons excited to virtual orbitals in the ground-state wave function for (i) C 2 ; (ii) N 2. Explain. Untuk satu fungsi gelombang complete active space self-consistent-field (CASSCF) yang mana orbital-orbital aktif diambil daripada orbital-orbital atom 2s and 2p, nyatakan bilangan elektron-elektron aktif dan bilangan maksimum elektron-elektron teruja ke orbital-orbital maya di dalam fungsi gelombang keadaan asas untuk (i) C 2 ; (ii) N 2. Terangkan. (6 marks/markah) 12. According to Koopman s theorem, the ionisation energy of a molecule is given by - i, minus the energy of the molecular orbital from which the electron is removed. This energy is given by: Berdasarkan kepada teorem Koopman, tenaga pengionan bagi satu molekul diberi oleh - i, tolak tenaga orbital molekul dari mana elektron itu disingkirkan. Tenaga ini diberi oleh: i h ii n elec j i J ij K ij Explain what each of the terms in this equation corresponds to in terms of the underlying physics. Hence give a qualitative justification for the applicability of this expression. Terangkan apakah setiap terma-terma di dalam persamaan ini daripada segi fiziknya. Dengan demikian, berikan justifikasi kualitatif daripada segi penggunaan ungkapan ini. (8 marks/markah) ***************