Q. How to determine the thresholds for the exponential generation of the higher-order excitation operators?

 

A. Higher-order linked excitation operators up to sextuples are generated by the exponential generation scheme described in the following papers:

H. Nakatsuji, Chem. Phys. Letters, 177, 331 (1991).

H. Nakatsuji, J. Chem. Phys. 83, 713, 5743 (1985).

H. Nakatsuji, J. Chem. Phys. 94, 6716 (1991).

See also description about EGOP in the Part II-C of the SAC-CI guide. Single excitation operators are included without selection. Doubles are handled as in SD-R part of the program. Higher-order excitation operators are generated as the products of A and B operators, R=A*B, A*A*B. The A and B operators are single and double excitation operators and selected with a criterion explained below.

  The second-order product generates triple and quadruple excitation operators.

R=A(S)*B(D) and A(D)*B(S),   triples

A(D)*B(D)                quadruples

“S” and “D” denote single and double excitation operators, respectively. The A-operators used for the second-order products are single and double excitation operators whose coefficients in the reference SD-CI wave function are larger than given thresholds

CThreEgABAOp=(A1Op=<thrma1>,A2Op=<thrma2>).

The <thrma1> and <thrma2> are thresholds for the single and double excitation operators, respectively.

  The third-order product generates quintuple and sextuple excitation operators.

R=A(D)*A(D)*B(S) and A(D)*A(S)*B(D),   quintuples

A(D)*B(D)*B(D)                      sextuples

The A-operators used for the third-order product are also single and double excitation operators whose coefficients in the reference SD-CI wave function are larger than given thresholds

CThreEgAABAOp= (A1Op=<thmma1>,A2Op=<thmma2>).

The <thmma1> and <thmma2> are thresholds for the single and double excitation operators, respectively.

For B-operators, the thresholds are given by

CThreEgAB=(B1Op=<thrmb1>,B2Op=<thrmb2>) for the second-order product and

CThreEgAAB=(B1Op=<thmmb1>,B2Op=<thmmb2>) for the third-order product.

The <thrmb1> and <thmmb1> are thresholds for the single excitation operators, and the <thrmb2> and <thmmb2> are those for the double excitation operators.

Thus, the accuracy of the exponential generation of the higher R operators in the general-R method is expressed by a set of the thresholds,

(<thrma1>, <thrma2>, <thmma1>, <thmma2>) and

(<thrmb1>, <thrmb2>, <thmmb1>, <thmmb2>).

The default values are

(<thrma1>, <thrma2>, <thmma1>, <thmma2>)=(0.04, 0.04, 0.1, 0.1)

(<thrmb1>, <thrmb2>, <thmmb1>, <thmmb2>).=(0.04, 0.04, 0.1, 0.1)

These parameters can be defined for each spatial- (ISYM) and spin-symmetries (KSTATE). In addition, the linked operators up to quadruple are further filtered by the perturbation selection with a given threshold (EThreEgR or eseleg). For quintuple and sextuple excitation operators, no perturbation selection is performed.