Physical Chemistry Third Edition

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G. The Perturbation Method The perturbation method is applied to a problem in which the Hamiltonian operator can be written in t ...

1284 G The Perturbation Method The coefficients of the linear (first-degree) terms obey the relation: Ĥ′Ψ(0)n +Ĥ(0)Ψ(1)n E(1) ...

G The Perturbation Method 1285 This integral is called amatrix elementofĤ′, and is also denoted byHnj′. The second- order corre ...

1286 G The Perturbation Method (Ĥ(0)+λ̂H′)(Ψ (0) n,corr+Ψ (1) n λ+Ψ (2) n λ (^2) + ···) (E(0)+E(1)nλ+E(2)n λ^2 + ···)(Ψ(0)n +Ψ ...

G The Perturbation Method 1287 where we define thematrix elementofĤ′ Hmj′  ∫ Ψm(0),init∗ Ĥ′Ψ(0)j,initdq (G-29) We can rewrite ...

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H. The Hückel Method The Hückel method is a simple semi-empirical method for determining approximate LCAO molecular orbitals to ...

1290 H The Hückel Method whereψaandψbare two of the 2pzatomic orbitals. The integralSabis anoverlap integralifab, and is anorm ...

H The Hückel Method 1291 (3) we assume that forabHabhas one value, calledβ, whenaandbrepresent atoms that are bonded to each o ...

1292 H The Hückel Method Theccoefficients in these orbitals can be determined so that the orbitals are normalized. We omit this ...

I. Matrix Representations of Groups Matrix multiplication is completely analogous to operator multiplication: It is distributive ...

1294 I Matrix Representations of Groups The 3 by 3 matrix in Eq. (I-3) is a representative of̂C 2 , denoted byR(̂C 2 ). The repr ...

I Matrix Representations of Groups 1295 We can show that these matrices obey the same multiplication table as the symmetry opera ...

1296 I Matrix Representations of Groups Each member of anabelian group(a group in which all members commute with each other) is ...

I Matrix Representations of Groups 1297 I.4 Bases for Representations The last entry in each row of the character table for the ...

1298 I Matrix Representations of Groups There are several theorems and facts that give useful information about the irre- ducibl ...

I Matrix Representations of Groups 1299 If the 3dxz,3dyz,3dxy,3dx (^2) −y 2 , and 3dz 2 orbitals are used as a basis for theC 2 ...

1300 I Matrix Representations of Groups Theb 2 basis function can combine with the 2pyfunction on the oxygen, and the 2px functi ...

I Matrix Representations of Groups 1301 representation (it is the sum of unity for each diagonal element of the matrix). For exa ...