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general [2019/10/04 16:51] – [Format of the ''cat'' File] admin | general [2023/11/07 12:40] – mueller | ||
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====== Documentaion for SPFIT and SPCAT ====== | ====== Documentaion for SPFIT and SPCAT ====== | ||
+ | |||
Last local (HSPM) modification: | Last local (HSPM) modification: | ||
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Some of the details of the program are described in | Some of the details of the program are described in | ||
- | | + | <alert type=" |
+ | H. M. Pickett, "The Fitting and Prediction of Vibration-Rotation Spectra with Spin Interactions," | ||
+ | </ | ||
===== Format of Quantum Numbers ===== | ===== Format of Quantum Numbers ===== | ||
Line 13: | Line 16: | ||
Quantum numbers which are used in the files **can be given in several formats**: | Quantum numbers which are used in the files **can be given in several formats**: | ||
- | The field QNFMT in the cat file can be regarded as having 3 sub-fields: | + | The field QNFMT in the cat file can be regarded as having 3 sub-fields:\\ |
- | QNFMT = Q*100 + H*10 + NQN, in which NQN is the number of quanta per state, H is a binary code | + | **QNFMT = Q*100 + H*10 + NQN**, in which **NQN** is the number of quanta per state, |
- | to indicate which of the last three quantum numbers are half integer quanta | + | **H** is a binary code to indicate which of the last three quantum numbers are half integer quanta |
- | (1 indicates that F is half integer), and Q is the number in square brackets in the table below. | + | (1 indicates that F is half integer), and **Q** is the number in square brackets in the table below. |
- | The least significant bit of H refers to the F quantum number and is 1 if F is half integer. | + | The least significant bit of **H** refers to the F quantum number and is 1 if F is half integer. |
- | Qmod5 gives the number of principal quantum numbers, i.e. without those designating spin quanta. | + | **Q**mod5 |
- | Thus it is 0 for atoms, 1 for linear molecules in S states, 2 for symmetric rotors and linear molecules | + | Thus it is **0** for atoms, |
- | in states other than S, and 3 for asymmetric rotors.\\ | + | in states other than S, and **3** for asymmetric rotors.\\ |
Add 11 if several states are fit together. These can be vibrational or electronic states, different | Add 11 if several states are fit together. These can be vibrational or electronic states, different | ||
isotopomers etc.\\ | isotopomers etc.\\ | ||
- | Add 20 if two spins are coupled to Itot.\\ | + | Add 20 if two spins are coupled to I< |
Add 40 if [[aggregate|aggregate spin number n]] is used because the number of quantum numbers needed otherwise exceeds 6. | Add 40 if [[aggregate|aggregate spin number n]] is used because the number of quantum numbers needed otherwise exceeds 6. | ||
- | | + | <alert type=" |
- | | + | **Note:** These " |
+ | </ | ||
Examples for Q: | Examples for Q: | ||
Line 66: | Line 70: | ||
The length of the quantum number list is determined by the number of spins requested. | The length of the quantum number list is determined by the number of spins requested. | ||
The factoring of the Hamiltonian is determined by the parameter set. | The factoring of the Hamiltonian is determined by the parameter set. | ||
- | |||
- | |||
===== Format of the '' | ===== Format of the '' | ||
**line 1-NLINE [12|3, freeform]: | **line 1-NLINE [12|3, freeform]: | ||
- | |||
- | * QN = 12 integer field of quantum numbers. Interpreted in a multiple I3 format as the quantum numbers for the line (upper quanta first, followed immediately by lower quanta). Unused fields can be used for annotation. The entire field is printed in file.fit | ||
- | * FREQ = frequency in MHz or cm< | ||
- | * ERR = experimental error. | ||
- | > NOTE: Minus sign means that the frequency and error are in units of cm< | + | > QN = 12 integer field of quantum numbers. Interpreted in a multiple I3 format as the quantum numbers for the line (upper quanta first, followed immediately by lower quanta). Unused fields can be used for annotation. The entire field is printed in file.fit\\ |
+ | > FREQ = frequency in MHz or cm< | ||
+ | > ERR = experimental error. | ||
+ | <alert type=" | ||
+ | **NOTE:** Minus sign means that the frequency and error are in units of cm< | ||
+ | </ | ||
+ | > WT = relative weight of line within a blend **(normalized to unity by program)**. Not needed for unblended lines. If WT is not specifically given in the line file, **1/n** will be used by the program if **n** is the number of blended lines at the same frequency and following successively. | ||
- | * WT = relative weight of line within a blend **(normalized to unity by program)**. Not needed for unblended lines. If WT is not specifically given in the line file, **1/n** will be used by the program if **n** is the number of blended lines at the same frequency and following successively. | + | <alert type=" |
- | + | **NOTES:** If an end-of-file is encountered before all the lines are read in, NLINE is set to the number read to that point. If successive lines have the same frequency, the lines will be treated as a blend and derivatives will be averaged using WT/ERR. Any lines with format errors will be ignored. | |
- | > NOTES: | + | </ |
+ | The freeform input begins in column 37 and extends to the end of the line. | ||
+ | See the notes at the end of the next section for more on the freeform input. | ||
- | The freeform input begins in column 37 and extends to the end of the line. See the notes at the end of the | ||
- | next section for more on the freeform input. | ||
===== Format of the '' | ===== Format of the '' | ||
Line 107: | Line 111: | ||
**Option information beginning on line 3:** CHR, SPIND, NVIB, KNMIN, KNMAX, IXX, IAX, WTPL, WTMN, VSYM, EWT, DIAG | **Option information beginning on line 3:** CHR, SPIND, NVIB, KNMIN, KNMAX, IXX, IAX, WTPL, WTMN, VSYM, EWT, DIAG | ||
- | > CHR: character to modify parameter names file (must be in first column) sping.nam , default is **g**. **a** is used for Watson A set, **s** is used for Watson S set. Other character replaces the **g** in the name ' | + | > CHR: character to modify parameter names file (must be in first column) sping.nam , default is **g**. **a** is used for Watson A set, **s** is used for Watson S set. Other character replaces the **g** in the name ' |
- | + | > sign SPIND: If negative, use symmetric rotor quanta. If positive, use asymmetric rotor quanta (Sign ignored on all but first option line.)\\ | |
- | > sign SPIND: If negative, use symmetric rotor quanta. If positive, use asymmetric rotor quanta (Sign ignored on all but first option line.) | + | > mag SPIND = degeneracy of spins, first spin degeneracy in units digit, second in tens digit, etc. (If last digit is zero, spin degeneracies occupy two decimal digits and the zero is ignored.)\\ |
- | + | > sign NVIB: positive means // | |
- | > mag SPIND = degeneracy of spins, first spin degeneracy in units digit, second in tens digit, etc. (If last digit is zero, spin degeneracies occupy two decimal digits and the zero is ignored.) | + | > mag NVIB = number of states (e. g. vibronic; also possible: isotopomers etc.; **counted from zero !**) on the first option line, identity of the vibronic state on all but the first option line. (max. value = 99)\\ |
- | + | > KNMIN,KNMAX = minimum and maximum K values. If both = 0, then linear molecule is selected.\\ | |
- | > sign NVIB: positive means // | + | > IXX: binary flag for inclusion of interactions: |
- | + | > sign IAX: If negative, use I< | |
- | > mag NVIB = number of states (e. g. vibronic; also possible: isotopomers etc.; **counted from zero !**) on the first option line, identity of the vibronic state on all but the first option line. (max. value = 99) | + | |
- | + | ||
- | > KNMIN,KNMAX = minimum and maximum K values. If both = 0, then linear molecule is selected. | + | |
- | + | ||
- | > IXX: binary flag for inclusion of interactions: | + | |
- | + | ||
- | > sign IAX: If negative, use I< | + | |
> WTPL,WTMN = statistical weights for even and odd state | > WTPL,WTMN = statistical weights for even and odd state | ||
- | > mag IAX = axis for statistical weight ( 1=a, 2=b, 3=c, add 3 if K-odd are excluded, add 6 if K-even are excluded) | + | > mag IAX = axis for statistical weight ( 1=a, 2=b, 3=c, add 3 if K-odd are excluded, add 6 if K-even are excluded)\\ |
- | + | > VSYM: If positive, vibronic symmetry coded as decimal digits (odd digit means reverse WTPL with WTMN) example: 10 = ( v=0 even, v=1 odd) (Only works for the first nine states) (Value ignored on all but first option line.) If negative, signal that the next line is also an option line.\\ | |
- | > VSYM: If positive, vibronic symmetry coded as decimal digits (odd digit means reverse WTPL with WTMN) example: 10 = ( v=0 even, v=1 odd) (Only works for the first nine states) (Value ignored on all but first option line.) If negative, signal that the next line is also an option line. | + | |
> EWT = EWT0 + EWT1*100 = weight for states with 3-fold E symmetry. Ignore if EWT is negative (default) (WTPL and WTMN apply to A1 and A2 symmetry) | > EWT = EWT0 + EWT1*100 = weight for states with 3-fold E symmetry. Ignore if EWT is negative (default) (WTPL and WTMN apply to A1 and A2 symmetry) | ||
Line 142: | Line 136: | ||
> EWT0 = (2I+1)(I+1)(4I)/ | > EWT0 = (2I+1)(I+1)(4I)/ | ||
- | **NOTE:** These weights can be divided by a common multiple if the rotational partition function is divided by the same factor. The A1 and A2 states are for MOD(ABS(K)–EWT1, | + | <alert type=" |
- | + | **NOTE:** These weights can be divided by a common multiple if the rotational partition function is divided by the same factor. The A1 and A2 states are for MOD(ABS(K)–EWT1, | |
+ | </ | ||
< | < | ||
DIAG = | DIAG = | ||
Line 156: | Line 151: | ||
**NOTE:** For many cases only a single option line is needed. If different vibronic states have different spin multiplicity or different KMIN, KMAX additional lines are needed. Note that additional lines are signaled by the sign of VSYM. The first option line sets up the defaults for all the vibrational states, and subsequent option lines specify deviations from the default. It is possible to mix Boson and Fermion states in the same calculation, | **NOTE:** For many cases only a single option line is needed. If different vibronic states have different spin multiplicity or different KMIN, KMAX additional lines are needed. Note that additional lines are signaled by the sign of VSYM. The first option line sets up the defaults for all the vibrational states, and subsequent option lines specify deviations from the default. It is possible to mix Boson and Fermion states in the same calculation, | ||
</ | </ | ||
- | ==== Parameter lines: IDPAR, PAR, ERRPAR / LABEL ==== | + | |
+ | ====== Coding of the Parameters ====== | ||
+ | |||
+ | ===== Parameter lines: IDPAR, PAR, ERRPAR / LABEL ===== | ||
where IDPAR is a parameter identifier, PAR is the parameter value, ERRPAR is the parameter uncertainty, | where IDPAR is a parameter identifier, PAR is the parameter value, ERRPAR is the parameter uncertainty, | ||
Line 162: | Line 160: | ||
PARAMETER identifiers (IDPAR) are coded in decimal digitform in the order | PARAMETER identifiers (IDPAR) are coded in decimal digitform in the order | ||
< | < | ||
- | NFF, I2, I1, NS, TYP, KSQ, NSQ, V2, V1\\ | + | NFF, I2, I1, NS, TYP, KSQ, NSQ, V2, V1 |
- | for NVIB < 10 each element occupies one digit except TYP which occupies two digits, i.e.\\ | + | |
- | (((((((FF*10+I2)*10+I1)*10+NS)*100+TYP)*10+KSQ)*10+NSQ)*10+V2)*10+V1\\ | + | for NVIB < 10 each element occupies one digit except TYP which occupies two digits, i.e. |
- | for NVIB > 9: each element occupies one digit except TYP, V1, and V2 which occupy two digits, i.e.\\ | + | (((((((FF*10+I2)*10+I1)*10+NS)*100+TYP)*10+KSQ)*10+NSQ)*10+V2)*10+V1 |
- | (((((((FF*10+I2)*10+I1)*10+NS)*100+TYP)*10+KSQ)*10+NSQ)*100+V2)*100+V1 | + | |
+ | for NVIB > 9: each element occupies one digit except TYP, V1, and V2 which occupy two digits, i.e. | ||
+ | (((((((FF*10+I2)*10+I1)*10+NS)*100+TYP)*10+KSQ)*10+NSQ)*100+V2)*100+V1 | ||
</ | </ | ||
* NFF = Fourier flag (used for internal rotation) If NFF < 11, basic operator is multiplied by cos (NFF * 2p K< | * NFF = Fourier flag (used for internal rotation) If NFF < 11, basic operator is multiplied by cos (NFF * 2p K< | ||
Line 223: | Line 223: | ||
If IDPAR is less than zero the magnitude is taken. In SPFIT, the parameter value will be constrained to be a constant ratio of the preceding parameter value. In this way linear combinations of parameters can be fit as a unit. | If IDPAR is less than zero the magnitude is taken. In SPFIT, the parameter value will be constrained to be a constant ratio of the preceding parameter value. In this way linear combinations of parameters can be fit as a unit. | ||
- | |||
- | ===== Coding of the Parameters ===== | ||
===== Format of the '' | ===== Format of the '' | ||
Line 299: | Line 297: | ||
**NOTE:** Dipoles with SYM > 0 are assumed to be in units of Debye. Dipoles with SYM = 0 are assumed to be in units of a Bohr magneton. Dipoles which are even order in direction cosine or N are assumed to be imaginary, except between states with EWT1 = 1. Dipoles between states with EWT1 = (0,2), (2,0), and (2,2) are ignored, but the matrix elements are calculated using corresponding dipoles from states with EWT1 = 1 (see below). For ITYP = 7 or ITYP = 8, I1 is used for the Fourier order and not the spin type. The constant r is specified in the parameter set. The sign of the r parameter is used to designate a special symmetry for the Fourier series. If this sign is different for V1 and V2, then 0.5 is subtracted from the Fourier order. For example, if IDIP = 72012, the basic // | **NOTE:** Dipoles with SYM > 0 are assumed to be in units of Debye. Dipoles with SYM = 0 are assumed to be in units of a Bohr magneton. Dipoles which are even order in direction cosine or N are assumed to be imaginary, except between states with EWT1 = 1. Dipoles between states with EWT1 = (0,2), (2,0), and (2,2) are ignored, but the matrix elements are calculated using corresponding dipoles from states with EWT1 = 1 (see below). For ITYP = 7 or ITYP = 8, I1 is used for the Fourier order and not the spin type. The constant r is specified in the parameter set. The sign of the r parameter is used to designate a special symmetry for the Fourier series. If this sign is different for V1 and V2, then 0.5 is subtracted from the Fourier order. For example, if IDIP = 72012, the basic // | ||
</ | </ | ||
+ | |||
===== Format of the '' | ===== Format of the '' | ||
Line 334: | Line 333: | ||
> QN(6) = Quantum numbers for the state | > QN(6) = Quantum numbers for the state | ||
- | ===== Special | + | ====== Special |
+ | |||
+ | This program set will calculate a variety of interactions and transitions within a Hund's case(b) basis, including spin orbit interactions which change spin multiplicity. The operator N< | ||
+ | |||
+ | Use of the symmetries in this program takes some care, particularly for linear molecules where it may not be immediately obvious whether to use the b or the c axis to designate perpendicular operators. For consistency with the parity designation for the symmetric top quanta, the vibronic wave function should be chosen so that it is symmetric with respect to the //ab// plane. Then the //b// axis can be used for the inversion defining axis (i.e. IAX = 2 in the option lines of the .par and .var files can be used to define selection rules under inversion). With this choice, the symmetry of rotation lines in the D< | ||
+ | |||
+ | |A |even N for S and all N for all other even l (even parity l doublet)| | ||
+ | |B(a)|odd N for S and all N for all other even l (odd parity l doublet) | ||
+ | |B(b)|all N for all odd l (even parity l doublet) | ||
+ | |B(c)|all N for all odd l (odd parity l doublet) | ||
+ | |||
+ | For S< | ||
+ | |||
+ | The g, u symmetry for an electronic state is for the parity of the wave-function under inversion of the space fixed axes. The nuclear exchange symmetry, on the other hand, affects only the statistical weights and does not have any further impact on the factoring of the Hamiltonian. In general, if IAX = 2, WTPL will be the nuclear spin weight for the A and B(b) states, while WTMN will be the weight for the other two symmetries. For S< | ||
+ | |||
+ | The correlation between parity and e,f designations follow the recommendations of J. M. Brown //et al.//, //J. Mol. Spectrosc.// | ||
+ | |||
+ | | |odd spin multiplicity | ||
+ | |e|p = (–1)< | ||
+ | |f|p = (–1)< | ||
+ | |||
+ | An example of .var file for oxygen like molecule: | ||
+ | |||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | |||
+ | An example of .int file for oxygen like molecule: | ||
+ | |||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | '' | ||
+ | |||
+ | The quantum number correlations between Hund's case (b) and case (a) can be a bit confusing at first. For example in a doublet P state N=J-1/2 always correlates with W =3/2 and N=J+1/2 always correlates with W =1/2 on the basis of projection. For A < 0, e.g. OH, the projection-based correlation follows the energy ordering. For A>0, the lower energy state is N=J+1/2 and W =3/2 as long as J+1/2 < sqrt(A/2B). Above this J, N = J+1/2 and W =1/2 (based on projection) is higher in energy than and N=J-1/2 and W = 3/2. Therefore quantum number assignments based on projections lead to different quanta than those based on energy. For a triplet S state, N=J+1 correlates with S =0 based on projection, N=J correlates with an odd combination of S =1 and S =-1, and N=J-1 correlates with an even combination of S =1 and S =-1. | ||
+ | |||
+ | Since q multiplies the same operator as (B-C) / 2, it is possible to use the sign of q to determine whether there are more electrons in the ab plane (q > 0) or whether there are more electrons in the ac plane (q < 0). | ||
+ | |||
+ | Explicit approximate relationships for the parameters are: | ||
+ | |||
+ | |100100vv' | ||
+ | |100101vv' | ||
+ | |1vv' | ||
+ | |100400vv' | ||
+ | |400vv' | ||
+ | |200100vv' | ||
+ | |1200100vv' | ||
+ | |1200000vv' | ||
+ | |1200400vv' | ||
+ | |2200100vv' | ||
+ | |2200400vv' | ||
+ | |1100100vv' | ||
+ | |||
+ | The extra factors of S in the definition of the spin-spin interaction parameter l, i. e. a spin-spin interaction 2 l ( S< | ||
+ | |||
+ | ====== Special | ||
+ | |||
+ | The // | ||
+ | |||
+ | The //K// quantum numbers for // | ||
+ | |||
+ | ===== Simple Examples ===== | ||
+ | |||
+ | Example of parameter types for asymmetric rotors (assuming < 10 vibronic states): | ||
+ | |||
+ | |11 | ||
+ | |01 | ||
+ | |10000 | ||
+ | |10099 | ||
+ | |20099 | ||
+ | |30099 | ||
+ | |40099 | ||
+ | |299 |–D< | ||
+ | |1199 | ||
+ | |2000 | ||
+ | |600001 | ||
+ | |20000099 |N·I for second spin | | ||
+ | |120010099|S< | ||
+ | |220010099|1.5*c< | ||
+ | |220040099|0.25*(c< | ||
+ | |||
+ | Quadrupole and magnetic spin-spin interactions are defined to be traceless (i.e. c< | ||
- | ===== Special | + | '' |
+ | '' | ||
+ | '' | ||
+ | '' | ||
- | ===== Some Examples ===== | + | specifies c< |
- | ===== Installation Instructions ===== | + | ====== Installation Instructions |
The Makefile shows how the various files are to be linked. The programs have been tested with Microsoft Visual | The Makefile shows how the various files are to be linked. The programs have been tested with Microsoft Visual |