Comment on “Computation of the pseudorotation matrix to satisfy the Eckart axis conditions” [J. Chem. Phys. 122, 124103 (2005)]

Abstract

Response to "Comment on 'Computation of the pseudorotation matrix to satisfy the Eckart axis conditions' " [J.

Response to “Comment on ‘Computation of the pseudorotation matrix to satisfy the Eckart axis conditions’ ” [J. Chem. Phys. 122, 227101 (2005)]

“…And here our approach, which constructs R and U via the completely standard symmetric matrix diagonalization procedure of two auxiliary symmetric matrices, 2 differs both from the iterative procedure suggested by Pickett and Strauss 4 as well as from the analytic solution via the SVD proposed by Dierksen. 1 The final results necessarily coincide as all these approaches solve the problem. Thus by no means our solution is mathematically equivalent to the one in Ref.…”

Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice

“…Although there have been interesting theoretical developments, such as the application of geometric algebra to derive Eckart KEOs 13 , and a method of analytical differentiation of the rotation matrix transforming into the Eckart frame has been introduced [29][30][31] , practical application of the Eckart frame has remained brute force numerical work considerably complicated by employing an energy operator with little resemblance of the Eckart-Watson Hamiltonian. All approaches to incorporate the Eckart conditions into the nuclear motion Hamiltonian have assumed explicitly [17][18][19][20][21] or implicitly 13 a rotation matrix determined such that the Eckart-axis conditions [32][33][34][35][36][37][38][39][40] , which should not be mistaken for the (rotational) Eckart conditions, be satisfied. However, studies on the gateway Hamiltonian method [41][42][43] have shown another solution to this question: Projection.…”