Computation of the pseudorotation matrix to satisfy the Eckart axis conditions

A general solution for satisfying the Eckart axis conditions [C. Eckart, Phys. Rev. 47, 552 (1935)] is presented. The goal is to find such a pseudorotation matrix T that the vector product between the reference molecular conformation R and another transformed conformation r′ is zero [∑a ma ra′ × Ra =0; ra′ =T ra]. Our solution avoids the limitations of the earlier one [H. M. Pickett and H. L. Strauss, J. Am. Chem. Soc. 92, 7281 (1970)], which fails when one of the involved intermediate matrices is singular. We also discuss how to choose among the always nonunique pseudorotation matrices T the one that represents a true rotation for situations when an alignment of the two conformations is desired.