On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry

Table 10

Expressions of 𝓡_{−𝑘,𝑘′}(𝜑,𝜒,𝜓) for Cardan angles (𝑘,𝑘^′∈{1,2,3,4,5}≡𝑚,𝑚^′∈{1,3,4,6,8}).

	𝑘=1	cos2𝜑cos𝜒cos𝜓+sin2𝜑sin2𝜒2sin𝜓	𝑘=2	sin2𝜑cos𝜒cos𝜓−cos2𝜑sin2𝜒2sin𝜓
𝑘^′=1	𝑘=3	−cos𝜑sin𝜒cos𝜓+sin𝜑cos2𝜒sin𝜓	𝑘=4	sin𝜑sin𝜒cos𝜓+cos𝜑cos2𝜒sin𝜓
	𝑘=5	√3sin2𝜒2sin𝜓
	𝑘=1	−cos2𝜑sin𝜒sin2𝜓−sin2𝜑cos2𝜒−34cos2𝜓	𝑘=2	−sin2𝜑sin𝜒sin2𝜓+cos2𝜑cos2𝜒−34cos2𝜓
𝑘^′=2	𝑘=3	−cos𝜑cos𝜒sin2𝜓+sin𝜑sin2𝜒2cos2𝜓	𝑘=4	sin𝜑cos𝜒sin2𝜓+cos𝜑sin2𝜒2cos2𝜓
	𝑘=5	−√3cos2𝜒+14cos2𝜓
	𝑘=1	cos2𝜑sin𝜒cos2𝜓−sin2𝜑cos2𝜒−34sin2𝜓	𝑘=2	sin2𝜑sin𝜒cos2𝜓+cos2𝜑cos2𝜒−34sin2𝜓
𝑘^′=3	𝑘=3	cos𝜑cos𝜒cos2𝜓+sin𝜑sin2𝜒2sin2𝜓	𝑘=4	−sin𝜑cos𝜒cos2𝜓+cos𝜑sin2𝜒2sin2𝜓
	𝑘=5	−√3cos2𝜒+14sin2𝜓
	𝑘=1	−cos2𝜑cos𝜒sin𝜓+sin2𝜑sin2𝜒2cos𝜓	𝑘=2	−sin2𝜑cos𝜒sin𝜓−cos2𝜑sin2𝜒2cos𝜓
𝑘^′=4	𝑘=3	cos𝜑sin𝜒sin𝜓+sin𝜑cos2𝜒cos𝜓	𝑘=4	−sin𝜑sin𝜒sin𝜓+cos𝜑cos2𝜒cos𝜓
	𝑘=5	√3sin2𝜒2cos𝜓
	𝑘=1	√−sin2𝜑3cos2𝜒+14	𝑘=2	√cos2𝜑3cos2𝜒+14
𝑘^′=5	𝑘=3	√sin𝜑3sin2𝜒2	𝑘=4	√cos𝜑3sin2𝜒2
	𝑘=5	−3cos2𝜒−14