Differences

This shows you the differences between two versions of the page.

--- general [2019/10/04 17:11] – [Special Considerations for Linear Molecules] add text from old server admin
+++ general [2019/10/04 17:14] – [Some Examples] add infos admin
@@ Line 394: / Line 394: @@
 ===== Special  Considerations for 'l'-doubled States =====
-===== Some Examples =====
+The  //l//-doubled states must be specified in adjacent pairs. The EWT1 = 1 states are those with //K l// > 0, and EWT1 = 2 states are those with //K  l// <= 0. The sign of //K// represents the parity, as in the non //l//-doubled states. Operators should be only specified between vibrational states with EWT1 = (0,0), (0,1), (1,0), (1,1), (1,2), and (2,1). Operators between vibrational states with EWT1 = (0,2), (2,0), and (2,2) are ignored. Operators connecting vibrational states with different //'l'// obey the selection rule that '//K-l//' can only change by multiples of 3. Operators diagonal in //l// have no '//K-l//' selection rules. If EWT1 = 1 for both states and if the parameter would normally be implicitly imaginary (i.e. operators odd-order in angular momentum for the Hamiltonian, or even-order for the dipole moment), then the parameter is assumed to be real and the rotational operator is multiplied by the sign of '//l//<sub>z</sub>'. DIAG = 0 is not recommended on the first option line in the //par// file, since the first-order energy is not likely to ordered with //K.//
+The //K// quantum numbers for  //l//-doubled states are designated specially when asymmetric rotor quanta are used so that the lower //K// doublet is associated with the EWT1 = 1 state and the upper //K// doublet and //K// = 0 states are assiciated with EWT1 = 2.  In this way the degenerate states have the same quantum numbers.
+=====  Simple Examples =====
+Example of parameter types for asymmetric rotors (assuming < 10 vibronic states):
+|11       |energy for v = 1                                                     |
+|01       |first order Fermi (F<sub>0</sub>) interaction between v = 0 and v = 1|
+|10000    |A<sub>00</sub>                                                       |
+|10099    |A (for all vibrational states)                                       |
+|20099    |B (dito)                                                             |
+|30099    |C (dito)                                                             |
+|40099    |0.25*(B – C)  (if prolate basis selected)                            |
+|299      |–D<sub>J</sub>                                                       |
+|1199     |–D<sub>JK</sub>                                                      |
+|2000     |–D<sub>K</sub> for v = 0                                             |
+|600001   |i N<sub>c</sub> interaction between v = 0 and v = 1                  |
+|20000099 |N·I for second spin                                                  |
+|120010099|S<sub>a</sub> I<sub>a</sub>                                          |
+|220010099|1.5*c<sub>zz</sub> for second spin                                   |
+|220040099|0.25*(c<sub>xx</sub>–c<sub>yy</sub>) for second spin                 |
+Quadrupole and magnetic spin-spin interactions are defined to be traceless (i.e. c<sub>xx</sub> + c<sub>yy</sub> + c<sub>zz</sub> = 0 or T<sub>xx</sub> + T<sub>yy</sub> + T<sub>zz</sub> = 0). Therefore, all three components cannot be fit simultaneously. The most efficient choice of parameters is shown in the table below. In cases where the user wants an alternative, it is possible to use constrained parameters. For example, to fit c<sub>aa</sub> and c<sub>cc</sub> (with no multipliers):
+''%% 220010099   100.%%''\\
+''%%–220020099  –100.%%''\\
+''%% 220030099    50.%%''\\
+''%%–220020099   –50.%%''
+specifies c<sub>aa</sub> = 100, c<sub>cc</sub> = 50, and c<sub>bb</sub> = –150.
 ===== Installation Instructions =====