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Orientation of the Eckart frame in a polyatomic molecule by symmetric orthonormalization
Author(s) -
Jørgensen Flemming
Publication year - 1978
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560140106
Subject(s) - orthonormal basis , orthonormality , orientation (vector space) , property (philosophy) , physics , frame (networking) , set (abstract data type) , mathematics , geometry , quantum mechanics , computer science , telecommunications , philosophy , epistemology , programming language
The Eckart frame is a frame of orthonormal vectors e i , i = 1, 2, 3, which follow a vibrating molecule while it rotates. The frame is orientated by the so‐called Eckart condition, which Eckart found by requiring the Coriolis interaction to be minimal. In the present paper we shall see that Eckart's frame also can be characterized by a simple least squares property. Eckart showed how to construct the e i 's by a certain orthonormalization of three vectors F i , i = 1, 2, 3. We observe that this orthonormalization is in fact Löwdin's symmetric. Then we consider the least squares property in the light of the Carlson‐Keller theorem—which is given a slightly different form. It is shown that the complete solution to Eckart's condition can be generated from the one of interest by C 2 rotations around axes in an orthonormal set which originates from the F i 's by Löwdin's canonical Orthonormalization.