12_variation_perturbation_matrixhq

000 hamiltonian matrix is not diagonal it must be

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Unformatted text preview: x) dx 1.000 x 0 a now all of the basis functions contribute to each wavefunction 0 c1i 2 a ( i 1) x a a 2 1( x) dx 1.000 sin i 2( x) 0.230 0.582 0.609 c2 0.471 0.118 0.028 0 c2i 2 a ( i 1) x a a 2 2( x) dx 1.000 sin i 0 1.5 x 0( x) .2 E v 1( x) .2 E v 1 1 eigenfunctions are not the basis functions 2( x) .2 E v 2 Ev E v 1 0.5 E v 2 0 0 2 4 6 8 10 x 14 10/7/2013 Ramp Potential x Matrix of Eigenvectors Diagonalizes the Hamiltonian 0 a C eigenvecs ( H) 0.400 0.000 0.000 1 C H C 0.000 0.000 0.000 inverse of C 0.000 0.000 0.000 0.000 0.000 2.348 0.000 0.000 0.000 0.000 0.000 0.701 0.000 0.000 0.000 0.000 0.000 0.976 0.000 0.000 0.000 0.000 0.000 0.000 1.753 0.000 0.000 0.000 1.314 0.000 Similarity Transformation 0 det 0 With basis set , , , where ∗ ∗ Schrödinger equation in matrix form solve secular equation to get energies 1,2, … , then the matrix elements of H and S are most molecular orbital techniques use all real basis functions and non-orthogonal basis sets energies are the eigenvalues of the matrix H-ES wavefunctions are the eigenvec...
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