Table Of Content

CONTENTS 1. ELEMENTARY QUANTUM CHEMISTRY... cccccccccccccccccccccccccccece 1.1. PRINCIPLES OF QUANTUM MECHANICS... ccccccccccccccccccccece 1.2. APPROXIMATE METHODS OF QUANTUM MECHANICS... cccccccccvces 1.2.1 Perturbation Theory for Stationary States......... 1.2.2 Perturbation Theory for Degenerate States......... 1.2.3 Linear Variation Method... ..ccccccccccccccccsscces 1.2.4 Nonlinear Variation Method.......cccccccccccsccces 1.2.5 Partitioning Method... cccccccsccscsedseessovssscoce 1.2.6 Method of Effective Hamiltonian.......2ccccceeceees SYMMETRY IN QUANTUM MECHANICS... cccccccccccccccscccccsecce 1.3.1 Symmetry of Molecules... cccccccccsccccccccccccccee 1.3.2 Reduction of Matrix Elements.......ccccccccccscces ONE-ELECTRON APPROXIMATION... cccccccccccccccccccccccscces 1.4.1 Many-Electron Systems... ccccccccccccccccsccccs 1.4.2 Blectron Configssaudcedris ateet ddsi tidoietnievisecc es 1.4.3 Matrix Elements of Operators......ccccccccccccccces 1.4.4 Hartree-Fock Equations.....ccccccccccccccccccccces 1.4.5 Density Functional Theory........ccccccccccccccces FREE ATOM. cc ccccccccccccc ccc ecs ccecec cccc cccc cc cccc ccccc es 1.5.1 Electron Configuration of a Free Atom............. 1.5.2 Bnergies Of Atomic TOLMBs cc osc hci obsseccscccrseces 1.5.3 Spin-Orbit Interaction in AtomsS......ccccccccccces CRYSTAL FIELD Pt -_.- teen heoee debe es 6084480060 a eee 1.6.2. Moak Cemeteal Bields oc. ccc cd tesilde dbi LER ceL b OSS 1.6.3. Strong Ceryutal Field. -ccccccbsec ieddsetbec v is 1.6.4 Improvements and Limits of the Crystal Field THEOLY. cccccccccccccccccccccccccscccccsccccccsceces EMPIRICAL MODELS... ccccccccccccccccccccccccccccccccccesccs 1.7.1 Ligand Field Theory...cccccccccccccccccccccccccccce 1.7.2 Angular Overlap Method... .cccccccccccccccccccccces REFERENCES... cccccccccccccccecec ccecec ccecec ecee crececec ecee cecc es 2. THE NATURE OF THE CHEMICAL BOND... ccccccccccccccccccccccces 2.1. MOLECULAR HAMILTONIAN... cccccccccccccccccccccccccccccccce 2.1.1 Isolated Molecule.ccccccccccccccccccscccccccscccccs 2.1.2 Effect of External Magnetic Field..............00- 2.1.3 Inelusion Of the Spine ccccccvcecéecsdsecseccoseseooes ye Pe Relativistic TOR. «..« diate atalalaletete elaliea ht taiale «ada dae es BORN-OPPENHEIMER APPROXIMATION... ccccccccccccscccscceceeell4 2.2.1 Classification of Molecular Motions.........e.ee+++-104 2.2.2 Separation of Electron and Nuclear Motion.........106 2.2.3 Adiabatic Potential... .cccccccccccccccccccsccccceelO9 MOLECULAR VIBRATIONS. .ccccccccccccccccccccecccceccscecccokld UTILIZATION OF THE ADIABATIC POTENTIAL......ccccccccceeelel 2.4.1 Properties of the Adiabatic Potential.............117 2.4.2 Thermodynamic and Kinetic Parameters.........+.2+-+-124 2.4.3 Molecular MechanicS....cccccccccccccccccccccccceeel28 JAMM-TELLER .BEPECE occ ccc cesses eisedsvesesesstisecccsscccsesha 2.5.1 Vibronic Coupling... ccccccccccccccccccces 2.5.2 Approximations to E - (a, + e) VAIBEFORLG COUPLINGe cecscvccvscovcccvescvcccsccesccclehd 2.5.3 Symmetry Descent Concept... cecccccccevccceeee el 5D 2.5.4 Calculation of Vibronic Constants..........2.2..2.+--156 2.5.5 Dynamic Jahn-Teller Effect... .cccccsccccccccesee el 59 BOUND STATES OF MOLECULES... .ccccccccccccccccccccseseseelbl 2.6.1 Physical Origin of the Chemical Bond..............161 2.6.2 Specific Features of Coordination Bond............166 SYMMETRY IN CHEMICAL REACTIONS... cccccccccccccsccccsesell2 2.7.1 Woodward-Hoffmann Rules... ..ccccccccccccvvcsccseeels3 2-7-2. BPreomtier OFbital THOSE oi sc ccc cseivcvwccccccccccclLs 7 8 2.7.3 Catalysis of Symmetry Forbidden Reactions.........180 227-6 - DapOLOGLOED BOOT OOOE 6 vic dc vice ee towsececscvececeLsBS ee re ne ee ee 3. MOLECULAR ORBITAL GE Ta ere ee ee Fe a ee | | | LCAO APPROXIMATION. cccccccccccccsccccsccccccccccccccccccselI l 3i1. 3.1.1 Charge Density Bond—Order Matrix......cceeeceeeeLeI] 3.1.2 Roothaan Method for Closed-Shell Systems..........194 3.1.3 Unrestricted Hartree-Fock Method.......ceceeeeeeele9D 7 3.1.4 Restricted Hartree-Fock Method.......cccccceseeeeleLD D 3.1.5 Half-Electron Method...cccccccccccccecscccccccscsccesll pe eei e eS 8! Ss ro er Detet BE Bs 6 i 6 66:6 00.65 60046 66600 044000 666 o0 e088 2 08 eee 3.2.2 Self-Consistent Field Procedure...................218 HMON-EMPIRICAL METHODS .ccccccccccscccccsesccsccccescecscectcal 3.3.1 Floating Spherical Gaussian Orbitals..............227 3.3.2 Pseudopotential Methods.....cccccccccccccccccceccelead Deded . Ba Met Nebesc-o:0-0-0:0 0a cee Cece olde KO e Seen ed eeweece eben 3.3.4 NEMO and Fenske-Hall Method........cccccecccvev2e 2e4 3 METHODS OF ZERO DIFFERENTIAL ving ss oat scdebicrdddae's ss Ee 3-464 ZDO APPTOKIMACION. oc ccccccccceve sews Co csss coccscccsee 3.4.2 Principles of Semiempirical Parametrization.......248 3.463. CHDO Methods. cscisccccasrvcsavde cbiovvvscbdscocccsctee 3.4.4 INDO Method... ccssessccsereesev deesesssscsccrese esct ed 3.4.5 NDDO and MNDO Method. .csssccccicsccscssvscscccscccsstO 3.4.6 Comparison of NDO Methods......ccccccccccccccesee2e8 0 BETENDED BOCKEE METHOD iiss oo ks oko STR eV s cA cows ee eR INCLUSION OF RELATIVISTIC EFFECTS... ..c.ccccccccccccceeeee dad 3.6.1 Dominant Relativistic Terms.......ccccccccsseeeee2e09 3.6.2 Spin-Orbit Interoias ccccstecceicseovvcnvccsccc.ccd be MOLECULAR ORBITAL PROPERTIES... ccccccccccscccscccsccccscecceedsi ls 3.7.1 Canonical Molecular Orbitals........cccccceeeeeeeedl7 3.7.2 Localized Molecular Orbitals........ccccccccesesee323 3.7.3 Distribution of Electron Density..........2222++++328 Pee TLE 6 0 2 6 6 6 866 6 6S OO DSS Oe s OES) C4 8 FO 8% CHE we SUS cs 6 2 ts SO 4. ELECTRON os Urs sa eee eee ee. 4.1. CORRELATION ENERGY... ccccccccccccccccccccccccceccce ceco c34 5 4.2. VARIATIONAL CONFIGURATION INTERACTION... cccccccccccee e349 4.3. VALENCE-BOND METHOD... .ccccccccccccccccccccccccccccccce eco3 c0 0 4.4. MULTICONFIGURATION SCF METHOD... cccccccccceccccccccccee e300 4.5. MANY-BODY PERTURBATION THEORY... cccccccccccccsecssccceceeet02 4.6. COUPLED CLUSTER APPROACH... cccccccecccccccccccces 4.7. PAIR CORRELATION METHODS... cccccccccccccccccccccccccccedI 3 4.8. GREEN FUNCTION TECHNIQUE... ccccccccccccccccccccccccccceee 3IO 4.9. PCILO AND PCTS MCMC S. noe ob Wee ewe oe ce beets cece eo tee 4.10. CIPSI METHOD. .ccccccccccccccccccccccecscc cccccccc cccccc ecc3 0 G a os sh 08S 4G a oo Be oo 0.0 6 0 0 6 & llth a aed oSb welts 6000 + 6 ee APPENDICES - ATOMIC UNITS AND PHYSICAL CONSTANTS @eeeeoeeoeeesee2ese?tee7neeeeeseeeee@ 3 9 2 2. COORDINATE PS hot bes Se oa eS eee BAe ee ee A GUIDE THROUGH JUNGLE OF QUANTUM-CHEMICAL METHODS.......396 a. SUBJECT Serer + ek A Ree ER ie ee ee LIST OF ABBREVIATIONS AND SYMBOLS AO Atomic Orbital AOM Angular Overlap Method AP Adiabatic Potential CCA Coupled Cluster Approach CFT Crystal Field Theory CI Configuration Interaction CNDO Complete Neglect of Differential OverlapP DF Dirac-Fock Dirac-Slater Discrete Variation Method Double Zeta Extended Hiickel Theory Hybrid Atomic Orbital Green Function Generalized Valence Bond Intermediate Neglect of Differential Overlap Jahn-Teller Effect Linear Combination of Atomic Orbitals Ligand Field Theory Longuet-Higgins-Pople Localized Molecular Orbital Many-Body Perturbation Theory Multiconfiguration Self-Consistent Field Molecular Mechanics Molecular Orbital Neglect of Diatomic Differential Overlap Perturbative Configuration Interaction using Localized Orbitals Primitive Function Perturbation Theory Poly Zeta Relativistic Extended Hiickel Restricted Hartree-Fock Self-Consistent Field Slater-Condon Parameter Spin-Orbit Interaction Slater-Type Orbital Single Zeta Unrestricted Hartree-Fock Valence Bond Zero Differential Overlap complex conjugate of a vector a operator of the physical quantity A mean value of the physical quantity A vector potential of electromagnetic field matrix with elements Aj, rPPPMPWlo rP inverse matrix to A | Kod transposed matrix to A, (A*) 5, =A ji hermitian conjugate to A, (A) 5. =A * ji ket vector bra vector column matrix (vector) row matrix (vector) antisymmetrization operator of n particles electron affinity of i-th orbital of atom A vector product of the vectors a and b scalar product of the vectors a and b commutator of the operators A and B anticommutator of the operators A and B magnetic field induction speed of light in vacuum matrix of LCAO coefficients dipole moment vector determinant of the matrix A elementary charge adiabatic potential electronic energy force constant matrix Fock operator electronic g-factor nuclear g-factor g two-electron operator electron interaction matrix Fourier transform of the one-electron Green function supermatrix of electron repulsion integrals Planck constant reduced Planck constant (h = h/2n) one-electron operator operator of the spin-orbit interaction imaginary unit unit matrix with the elements re J angular momentum of a nucleus ionization energy of i-th orbital of atom A two-electron integral of electron repulsion <ij|g|kl> two-electron integral of electron repulsion total angular momentum of electron Coulomb operator Coulomb integral over spinorbitals exchange operator exchange integral over spinorbitals Boltzman constant orbital angular momentum of electron mass of A-th nucleus mass of electron rest mass of a particle number of electrons number of atoms in a molecule Avogadro constant 25Q q. 2 occupied molecular (spin) orbital projection operator rd Q rg a) charge density (bond-order) matrix >HQ S linear momentum of a particle spin-free n-particle density function operator complementary to P gas constant spin angular momentum of electron o. overlap integral temperature yHD>w oHonyes kinetic integral yy qe> trace of the matrix A aUi—.~ matrix of a unitary transformation averaged integral of electron-nuclear attraction integral of electron-nuclear attraction LJ. wo < a unoccupied (virtual) molecular (spin) orbital Mulliken orbital electronegativity mM annihilation operator X creation operator Z proton number of A-th nucleus Z core charge in units of e cpD+bBh:Huo pUpo. p: spin-up function (m, = +1/2) spin-down function (m. = -1/2) Bohr magneton nuclear magneton Dirac operators (matrices of dimension 4 x 4) averaged integral of electron repulsion representation of a symmetry point group direct product of representations Kronecker symbol Dirac function parameter of the ligand-field strength vacuum permittivity orbital energy summation omitting the terms with i = j spin function orbital exponent atomic orbital wavelength Magnetic moment vector frequency of radiation wavenumber constant of the spin-orbit interaction charge density conversion factor to SI units (og; = e7/4ne,) ~ vector of Pauli matrices (ole Oye o,) Pauli matrix of dimension 2 x 2 molecular orbital electrostatic potential determinantal wave function (Slater determinant) of the electron configuration wave function of the monoexcited configuration wave function of the biexcited configuration primitive basis set function spinorbital wave (state) function vector operator 'nabla'