TY - JOUR
T1 - Computation of the pseudorotation matrix to satisfy the Eckart axis conditions
AU - Dymarsky, Anatoly Y.
AU - Kudin, Konstantin N.
PY - 2005/3/22
Y1 - 2005/3/22
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/17444418981
UR - https://www.scopus.com/inward/citedby.url?scp=17444418981&partnerID=8YFLogxK
U2 - 10.1063/1.1864872
DO - 10.1063/1.1864872
M3 - Article
AN - SCOPUS:17444418981
SN - 0021-9606
VL - 122
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 12
M1 - 124103
ER -