Based on Rayleighndash;Schrouml;dinger perturbation theory, eight general expressions of the triple perturbation energyegr;n,m,tare derived. The relationships among them give several general interchange theorems in a compact fashion. These interchange theorems exchange the integrals involving higherhyphen;order perturbed wavefunctions related to a complicated perturbationlgr;V, by integrals involving higherhyphen;order perturbed wavefunctions related to the simpler perturbations. From the perturbed wavefunction corrected to thenth order oflgr;V, (1) in general, the interchange theorems allow us to obtain the perturbation energy to thelpar;nthinsp;plus;thinsp;1rpar;thorder; (2) whenHdeg;andlgr;Vare Hermitian, the interchange theorems allow us to obtain the perturbation energy to thelpar;2nthinsp;plus;thinsp;1rpar;thorder; (3) whenHdeg;, lgr;V, and other perturbations are Hermitian, the interchange theorems will reduce the required total order of wavefunctions related to the Hermitian perturbations to almost half. These interchange theorems can be applied to any triple perturbation problem when the unperturbed state is nondegenerate. They are valid to all orders with respect to the three perturbations. The application of these interchange theorems to calculate special kind of secondhyphen;order physical properties,F, such as electric shielding factors, chemical shifts, and nuclear spinndash;spin coupling constants, is discussed. It is shown that if (1) the two perturbations associated with the properties are onehyphen;electron operators, and (2) the zerothhyphen;order wavefunction of a closedhyphen;shell system is obtained by SCF method, then the firsthyphen;order correction ofFis determined solely by the firsthyphen;order orbitals,i0,1,0andi0,0,1, related separately to the two perturbations but does not depend on any ldquo;crossrdquo; secondhyphen;order orbitals,i0,1,1. This result will simplify the calculation very much.
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