Intrinsic reaction coordinate IRC or statics

The phase appears, when the system makes a trip in configurational space. We may make the problem of the Berry phase more familiar by taking an example from everyday life. Let us take a 3D space. Please put your arm down against your body with the thumb directed forward. During the operations described below, please do not move the thumb with respect to the arm. Now stretch your arm horizontally sideways, rotate it to your front and then put down along your body. Note that now your thumb is not directed towards your front anymore, but towards your body. When your arm has come back, the thumb had made a rotation of 90°. 

Your thumb corresponds to (/ (/ R), i.e. a vector in the Hilbert space, which is coupled with a slowly varying neighbourhood R corresponds to the hand positions). When the neighbourhood returns, the vector may have been rotated in the Hilbert spaee [i.e. multiplied by a phase exp(/ ))]. 

This seetion addresses point 4 of our plan from p. 770. 

770 two reaetion coordinates were proposed DRC and SDP. Use of the first of them may lead to some serious difficulties (like energy discontinuities). The second reaction coordinate will undergo in a moment a useful modification and will be replaced by the so called intrinsic reaction coordinate (IRC). 

Let us use the Cartesian coordinate rqrstem once more with 3N coordinates for the N nuclei Xi,i =, . 3N, where Xi, X-i, X denote the x, y, z coordinates of atom 1 of mass M, etc. The i-th coordinate is therefore associated with mass Mi of the eorresponding atom. The classical Newtonian equation of motion for an atom of mass M/ and coordinate Xi is  

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