Orthogonal wave functions

There exists today an alternative approach which has made MCSCF calculations on excited states feasible, also for rather large systems. A method has been developed which makes it easy to obtain orthogonal wave functions and transition densities from CASSCF wave functions optimized independently for a number of excited states of different or the same symmetry as the ground state. The method has been called the CAS State Interaction (CASSI) method. It will be briefly described below. 

Since the two wave functions overlap, we can form from them two orthogonal wave functions using the Graham—Schmidt orthogonalization procedure,... 

A wave function satisfying this equation is a function of the time and of the coordinates of the system. For a given value of t, say t, f it ) is a function of the coordinates alone. By the general expansion theorem of Section 22 it can be represented as a series involving the complete set of orthogonal wave functions for the unperturbed system,... 

Equation (23.12) shows that when S is not zero (R is not infinite), i/ j and ij/n are not orthogonal. Consequently, they are no longer proper wave functions f or the system when R is not infinite. Two orthogonal wave functions can be constructed from and J/n by taking them in linear combination. These orthogonal wave functions serve as the first approximate wave functions of the system. 

In this book, the veetors to orfliogonalize will be the Efilbert space vectors (see Appendix B available at booksite.elsevier.com/978-0-444-59436-5) i.e., the normalized wave functions. In the case of two sueh vectors (pi and (p2 having the scalar product (pi (p2), we construct the new orthogonal wave functions - i = 0i, ip2 = — or = (pi — i)y... 

The interaction leads to the following orthogonal wave functions (C C2, D and D2 are coefficients) ... 

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