First-order cusp condition

An even more radical yet effective approximation to the R12 method was proposed by Ten-no [28,43], in which the coefficients multiplying the correlation function were held fixed at the values implied by the first-order cusp condition and hence were not to be determined iteratively or noniteratively. Several variants of the CCSD(T)-R12 methods were developed on the basis of this promising approximation by Adler et al. [68], Tew et al. [69], Bokhan et al. [70], and Torheyden et al. [66]. 

Curran [61C01] has pointed out that under certain unusual conditions the second-order phase transition might cause a cusp in the stress-volume relation resulting in a multiple wave structure, as is the case for a first-order transition. His shock-wave compression measurements on Invar (36-wt% Ni-Fe) showed large compressibilities in the low stress region but no distinct transition. 

Physically, C, which controls the large wavevector decay of ( / i, depends on the behavior of the system at small interelectronic separations. In fact, C is proportional to the system-average of the cusp in the exchange-correlation hole at zero separation. If smooth function of r - r, then g x(r, r) = 0, and C would vanish, as it does at the exchange-only level (i.e., to first order in e2). However, as we saw in section 2.2, the singular nature of the Coulomb interaction between the electrons leads to the electron-coalescence cusp condition, Eq. (31). For the present purposes, we wish to keep track explicitly of powers of the coupling constant, so we rewrite Eq. (31) as... 

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