2. Many-electron systems
... We call this procedure as Self-Consistent Field (SCF), since the field (electron-electron interaction) generated by orbitals gives the same orbitals. P Total energy: E 6= i εi , i.e. not a sum of the orbital energies since in this case we would count electron-electron interaction twice. Therefore, w ...
... We call this procedure as Self-Consistent Field (SCF), since the field (electron-electron interaction) generated by orbitals gives the same orbitals. P Total energy: E 6= i εi , i.e. not a sum of the orbital energies since in this case we would count electron-electron interaction twice. Therefore, w ...
Electrophilic Additions to Double Bonds
... Hamiltonian for an orbital is the orbital energy each orbital sees the average distribution of all the other electrons finding a many electron wavefunction is reduced to finding a series of one electron orbitals ...
... Hamiltonian for an orbital is the orbital energy each orbital sees the average distribution of all the other electrons finding a many electron wavefunction is reduced to finding a series of one electron orbitals ...
Lecture 2
... The Hartree 1-electron equation needs to be solved “self-consistently” to obtain the solutions (i.e., ei and i) for all the electrons! Why? Because the Hartree potential is written in terms of the solutions Thus, Hartree “guessed” the solutions, used these guesses to compute the Hartree potential, ...
... The Hartree 1-electron equation needs to be solved “self-consistently” to obtain the solutions (i.e., ei and i) for all the electrons! Why? Because the Hartree potential is written in terms of the solutions Thus, Hartree “guessed” the solutions, used these guesses to compute the Hartree potential, ...
Chapter 7 Handout 1 Atomic Orbitals Quantum Numbers: Principal
... Rules for filling orbitals: 1. Aufbau Principle: a. Electrons fill up orbitals of lowest energy first b. Orbitals in the same sublevel are equal in energy c. Sometimes energy levels overlap 2. Pauli Exculsion Principle a. There is a max of 2 electrons in any one orbital b. These 2 electrons must ha ...
... Rules for filling orbitals: 1. Aufbau Principle: a. Electrons fill up orbitals of lowest energy first b. Orbitals in the same sublevel are equal in energy c. Sometimes energy levels overlap 2. Pauli Exculsion Principle a. There is a max of 2 electrons in any one orbital b. These 2 electrons must ha ...
some approximation
... 4. Multiple determinants. We can't live with them, we can't live without them. ...
... 4. Multiple determinants. We can't live with them, we can't live without them. ...
Chem700 MO
... Solving the Roothaan-Hall Equations 1. choose a basis set 2. calculate all the one and two electron integrals 3. obtain an initial guess for all the molecular orbital coefficients Ci 4. use the current Ci to construct a new Fock matrix 5. solve F Ci = i S Ci for a new set of Ci 6. if the new Ci a ...
... Solving the Roothaan-Hall Equations 1. choose a basis set 2. calculate all the one and two electron integrals 3. obtain an initial guess for all the molecular orbital coefficients Ci 4. use the current Ci to construct a new Fock matrix 5. solve F Ci = i S Ci for a new set of Ci 6. if the new Ci a ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 12) Evaluate ( um, x un) where un’s are the eigenfunctions of a linear harmonic oscillator. 13) Prove that “the momentum operator in quantum mechanics is the generator of infinitesimal translations”. 14) (a) Prove that ( σ.A) (σ.B) = A.B + i σ. ( A xB) where σ’s are the Pauli spin matrices , if the ...
... 12) Evaluate ( um, x un) where un’s are the eigenfunctions of a linear harmonic oscillator. 13) Prove that “the momentum operator in quantum mechanics is the generator of infinitesimal translations”. 14) (a) Prove that ( σ.A) (σ.B) = A.B + i σ. ( A xB) where σ’s are the Pauli spin matrices , if the ...
Chapter 9 – Many Electron Atoms
... One always needs to go beyond HF to get quantitatively accurate results ...
... One always needs to go beyond HF to get quantitatively accurate results ...
Quantum Model Worksheet
... Quantum Model of the Atom – Ch. 4 (p. 98 – 104) PART A – WAVES & QUANTUM MECHANICS 1. What experimental evidence supported de Broglie’s idea that electrons have wave-like properties? ...
... Quantum Model of the Atom – Ch. 4 (p. 98 – 104) PART A – WAVES & QUANTUM MECHANICS 1. What experimental evidence supported de Broglie’s idea that electrons have wave-like properties? ...
Quantum Model Worksheet
... Quantum Model of the Atom – Ch. 4 (p. 104-110) PART A – WAVES & QUANTUM MECHANICS 1. What experimental evidence supported de Broglie’s idea that electrons have wave-like properties? ...
... Quantum Model of the Atom – Ch. 4 (p. 104-110) PART A – WAVES & QUANTUM MECHANICS 1. What experimental evidence supported de Broglie’s idea that electrons have wave-like properties? ...
An Overview of Computational Chemistry
... •The total wave function is limited to one electronic surface, i.e. a particular electronic state. •The BO approx. is usually very good, but breaks down when two (or more) electronic states are close in energy at particular nuclear geometries. •In such situations, a “ non-adiabatic” wave function - ...
... •The total wave function is limited to one electronic surface, i.e. a particular electronic state. •The BO approx. is usually very good, but breaks down when two (or more) electronic states are close in energy at particular nuclear geometries. •In such situations, a “ non-adiabatic” wave function - ...
Molecular Quantum Chemistry
... Fock operator depends on occupied MO’s only; l The procedure produces Nbasis total MO’s; l ...
... Fock operator depends on occupied MO’s only; l The procedure produces Nbasis total MO’s; l ...
Physical Chemistry The hydrogen atom Center of mass
... The spatial part is incomplete One incorporates spin as a separate coordinate Wave function is a product n ,l ,m , I ,mI (r , , ) ...
... The spatial part is incomplete One incorporates spin as a separate coordinate Wave function is a product n ,l ,m , I ,mI (r , , ) ...
Physical Chemistry The hydrogen atom Center of mass
... 1 hartree 27.2114 electron volts 1 rydberg 13.606 electron volts ...
... 1 hartree 27.2114 electron volts 1 rydberg 13.606 electron volts ...
Section 5-2
... • Compare the Bohr and quantum mechanical models of the atom • Explain the impact of de Broglie’s waveparticle duality and the Heisenberg uncertainty principle on the modern view of electrons in atoms • Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals ...
... • Compare the Bohr and quantum mechanical models of the atom • Explain the impact of de Broglie’s waveparticle duality and the Heisenberg uncertainty principle on the modern view of electrons in atoms • Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals ...
Ch 1 Lecture 2
... a) “Wave Functions” (Y) are solutions to the wave equations b) Y2 = probability of finding e- at each point in space 3) Atomic Orbitals a) e- locations are quantized, not found everywhere but only at certain energies b) 3-D plots of the wave functions indicate where the electron is likely to be foun ...
... a) “Wave Functions” (Y) are solutions to the wave equations b) Y2 = probability of finding e- at each point in space 3) Atomic Orbitals a) e- locations are quantized, not found everywhere but only at certain energies b) 3-D plots of the wave functions indicate where the electron is likely to be foun ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 /1.00-4.00
... 11. Discuss the failures of classical mechanics and the success of quantum theory in the explanation of black body radiation. . 12. What are quantum mechanical postulates? Explain briefly any two of the postulates. 13. The work function for Cesium is 2.14 eV. What is the kinetic energy and the speed ...
... 11. Discuss the failures of classical mechanics and the success of quantum theory in the explanation of black body radiation. . 12. What are quantum mechanical postulates? Explain briefly any two of the postulates. 13. The work function for Cesium is 2.14 eV. What is the kinetic energy and the speed ...
Advanced Physical Chemistry
... of another basis set. From a set of M basis functions , obtain M linearly independent spatial wavefunctions. End up solving the Roothaan equations, which are solved form the secular determinant. One and two electron integrals are part of the matrix. For M basis functions, there are M4 two-electron o ...
... of another basis set. From a set of M basis functions , obtain M linearly independent spatial wavefunctions. End up solving the Roothaan equations, which are solved form the secular determinant. One and two electron integrals are part of the matrix. For M basis functions, there are M4 two-electron o ...
EX3504-03
... a. MP4 is a variation method. b. The bond order of H2 is ½. c. Hartree-Fock method includes all electron-electron correlation. d. 6-31G calculations usually yield better results than 3-21G calculations. e. DFT is a better method because it needs less computational time than Hartree-Fock method. Prob ...
... a. MP4 is a variation method. b. The bond order of H2 is ½. c. Hartree-Fock method includes all electron-electron correlation. d. 6-31G calculations usually yield better results than 3-21G calculations. e. DFT is a better method because it needs less computational time than Hartree-Fock method. Prob ...
Specialization: 010600/52 Program: Applied Mathematics and Physics Program director: prof. S.L. Yakovlev
... problem itself. The aim of the present work is to explore deal.II and to evaluate its efficiency, stability and accuracy for quantum mechanical problems. The helium atom with zero total angular momentum has been chosen as a benchmark of the three-body Coulomb problem. Both the exact threedimensional ...
... problem itself. The aim of the present work is to explore deal.II and to evaluate its efficiency, stability and accuracy for quantum mechanical problems. The helium atom with zero total angular momentum has been chosen as a benchmark of the three-body Coulomb problem. Both the exact threedimensional ...
H - unix.eng.ua.edu
... SIMPLIFICATION: BO approximation – decouple motions of nucleus and the electrons. Valid Assumption? Electron motion is much faster than nucleus (mass ratio ~ 1800) Electron relaxation is essentially instantaneous. Result – electronic Schrödinger equation: ...
... SIMPLIFICATION: BO approximation – decouple motions of nucleus and the electrons. Valid Assumption? Electron motion is much faster than nucleus (mass ratio ~ 1800) Electron relaxation is essentially instantaneous. Result – electronic Schrödinger equation: ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... a simple solution, which assumes the wave function to depend only on the distance r and not on θ and φ. b) The wave function of 1s orbital of Li2+ is Ψ1s = (1/√π) (Z/a0)3/2 exp(-Zr/a0), where a0 is the most probable distance of the electron from the nucleus and Z is the atomic number. Show that the ...
... a simple solution, which assumes the wave function to depend only on the distance r and not on θ and φ. b) The wave function of 1s orbital of Li2+ is Ψ1s = (1/√π) (Z/a0)3/2 exp(-Zr/a0), where a0 is the most probable distance of the electron from the nucleus and Z is the atomic number. Show that the ...
WAVE MECHANICS (Schrödinger, 1926)
... of matter and the uncertainty principle. * The state of an electron is described by a function y, called the “wave function”. * y can be obtained by solving Schrödinger’s equation (a differential equation): Hy=Ey ...
... of matter and the uncertainty principle. * The state of an electron is described by a function y, called the “wave function”. * y can be obtained by solving Schrödinger’s equation (a differential equation): Hy=Ey ...
3. Electronic structure of atoms
... the orbitals as 1s, 2s, 2p0 , 2p1 , 2p−1 , etc. The radial part: R(r) will differ, since the potential is different here than for the H atom: since it is not a simple Coulomb-potencial, the degeneracy according to l quantum number will be lifted, i.e. the orbital energies will depend not only on n b ...
... the orbitals as 1s, 2s, 2p0 , 2p1 , 2p−1 , etc. The radial part: R(r) will differ, since the potential is different here than for the H atom: since it is not a simple Coulomb-potencial, the degeneracy according to l quantum number will be lifted, i.e. the orbital energies will depend not only on n b ...