Computational chemistry May 2009

Computer & chemistry

In vitro = in glass, in a test tube In vivo = in the living, in living organism In silico = on computer, via computer sim Possible approaches – Semi empirical method – Ab initio method

SCF Self-consistent field procedures – Initial guss about the LCAO is refined until the solution remains unchanged example – At fixed nuclei positions – First guess of LCAO coefficients – Solve SE for the electrons – Results in estimate of LCAO coefficients – New MO and energy values – Repeat until no more changes

MO of Ethylene = LCAO of 2p

Coulomb / resonance integrals

Summary : Hückel MO Erich Hückel for the π orbitals of hydrocarbons Assumptions – overlap integrals S ij are set to zero unless i = j, when Sij = 1 – all the diagonal elements in the secular equation are assumed to be the same; thus, the Coulomb integrals Hij are all set equal to a – the resonance integrals H ij are set equal to zero, except for those on neighbouring atoms which are set equal to β.

Extended Hückel theory Removal of the restriction of the HT No more to planar hydrocarbon system EHT (1963) Expand to Heteroatomic non-planar system

CNDO Complete neglect of differential overlap – Further approximations of HT Similar methods – INDO Intermediate neglect of differential overlap – MNDO Modified neglect of differential overlap – AM1 Austin model 1 MINDO version 2

Ab initio method GTO – Gaussian type orbital for LCAO – Exp(-r) = real H-like atom orbital – Exp(-r 2 ) = gaussian function

Density Functional methods Advantage of DFT Less demanding computational effort Less computer time Better agreement for d-orbital complexes Electron density instead of wavefunction SE expressed in electron density Kohn-Sham equation (B3LYP and MPW1PW91) explicitly include correlation effects at the SCF level of calculation.

Graphical output Isodensity surface – A surface of constant total electron density Slicing the surface Electrostatic potential surface – Net positve charge/net negative charge in colors

Ball and stick model

Fused CPK spheres

Sticks with vdW dots

ChemDraw

Hyperchem 하이퍼켐 프로그램 – 분자 모델링 S/W – 분자구조에 대하여 정규모드 분석 – 가시화 및 동영상으로 확인 가능 – 분자의 Visualizing, Analyzing, Simulating 과 분자 구조에 대한 정보의 Communication 을 할 수 있는 Package. – 모델링 초보자에서부터 숙련된 Modeler 에 이르기까지 분자의 성질을 연구하고 예상할 수 있는 Tool Set 제공 – 분자의 구조와 에 대해 유용한 직관력을 제공

Hyperchem in Action Heat of formation Ionization potential Electron affinities Dipole moments UV/VIS spectra IR spectra

Model Building & Visualization 간단한 분자의 Draw 방법 – Metal Complex, Peptide 및 Nucleic acid Building – 외부 구조와 Interface – 다양한 Rendering 방법 제공 – 3 차원적으로 회전, 이동, 확대 및 축소 – Stereochemistry

Moleuclar display Import structures from standard file formats: – Brookhaven PDB, – ChemDraw CHM, – MOPAC Z-matrix, – MDL MOL and ISIS Sketch – Tripos MOL2 files. Display structures – ball and stick, – fused CPK spheres, – sticks, – van der Waals dots – sticks with vdW dots

Z-matrix input N H H H the first line only the atom name, a running number and the charge of the atom is given. The running number is only for ease of reference to a given atom, and is actually not used within the program, where any reference to an atom, is the number of the atom consecutively in the input list. The second line consists of the atom name, a running number, the number of the atom to which this atom is bonded with a given bond length, and then finally the charge of this atom. The third line is identical to the second, except that an extra atom number, to which the two first atoms on this line is bonded to with a given bond angle. On the fourth line yet another atom has been added, and the position of this atom relative to the three previous ones on this line is dependent upon on an extra number inserted just before the nuclear charge of this atom. If the next to last number is a 0, the position of this atom is given by the dihedral angle (A1,A2,A3,A4), where Ai denotes atom i. If, on the other hand, this next to last number is, the position of the fourth atom is given with respect to two angles, namely (A1,A2,A3) and (A2,A3,A4). The sign is to be if the triple product is positive.

Gaussian 미국 Gaussian Inc. 제품 선험적 분자궤도함수 계산 프로그램 다양한 컴퓨터에서 사용 가능 – 단일 위치에서 에너지 계산 (single point) – 에너지 최적화를 하면서 구조 계산 (optimize) – 진동 스펙트럼 정규진동 계산

Gaussian input file # HF/6-31G(d) OPT Route section water energy Title section 0 1 Molecule specification O H H

계산 방법 N 개의 원자핵과 n 개의 전자로 이루어진 분자에 대한 슈뢰딩거 방정식 – H = Σ( 전자의 T + 전자와 핵 사이의 포텐셜 ) + ( 전자간 반발 포텐셜 ) + ( 핵간 반발 포텐셜 ) – 근사적으로만 풀 수 있다 Hartree-Fock 근사 – 평균적으로 볼 때, 각각의 전자들은 독립적으로 운동한다고 가정 LCAO – Linear combination of atomic orbital (basis set) – 원자 파동함수를 기저함수 (basis set) 로 사용하여 분자 파동함수 구성

Variational theorem HΨ true = EΨ true Ψ * HΨ= Ψ * EΨ ∫Ψ * HΨ dτ = E∫Ψ * Ψ dτ =E 정확한 파동함수 Ψ true 를 모른다면 ? 시험용 함수 (trial wavefunction) 에 대해 항상 ∫Ψ * HΨ dτ ≥ E∫Ψ * Ψ dτ – LCAO 의 계수를 결정할 수 있다.

Calculation Methods – Hartree-Fock (HF) and HF with correlation corrections from Moller-Plesset perturbation theory (MP2, MP3, MP4 SDQ, and MP4 SDTQ)

example : Water Dimer Geometries water dimer geometries were established – by fixing the Oxygen atom separation Then performing a complete optimization of all other geometrical parameters. – Hartree-Fock level of theory using the G** basis set. Basis Set Selection – to establish what basis set we must use to get meaningful results. – the dimer binding energy results at the HF level of theory