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Explicitly correlated F12 methods using CUSP conditions

F12 methods based on the Slater-type geminal along with (complementary) auxiliary basis set ((C)ABS) or numerical quadratures (QD) for many-electron integrals lead to greatly improved convergence of correlation energies. Moreover the use of the s- and p-wave cusp conditions for geminal amplitudes directly (SP-Ansatz) leads to numerically stable and computationally efficient methods. The SP-Ansatz is somethimes called as fixed amplitudes or diagonal orbital invariant Ansatz. We will discuss MP2-F12, CCSD(T)(F12) for the ground state energies, and several EOM-CCSD(F12) methods for various energy differences using cusp conditions ​
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