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Some of the details of the program are described in | Some of the details of the program are described in | ||

- | H. M. Pickett, "The Fitting and Prediction of Vibration-Rotation Spectra with Spin Interactions," J. Mol. Spectros. 148, 371-377 (1991). | + | <alert type="info"> |

+ | H. M. Pickett, "The Fitting and Prediction of Vibration-Rotation Spectra with Spin Interactions," J. Mol. Spectros. 148, 371-377 (1991). | ||

+ | </alert> | ||

===== Format of Quantum Numbers ===== | ===== Format of Quantum Numbers ===== | ||

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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 ''lin'' File ===== | ===== Format of the ''lin'' File ===== | ||

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</alert> | </alert> | ||

- | ===== Coding of the Parameters ===== | + | ====== Coding of the Parameters ====== |

- | ==== Parameter lines: IDPAR, PAR, ERRPAR / LABEL ==== | + | ===== Parameter lines: IDPAR, PAR, ERRPAR / LABEL ===== |

where IDPAR is a parameter identifier, PAR is the parameter value, ERRPAR is the parameter uncertainty, LABEL is a parameter label (10 characters are used) that is delimited by **/. ** If the sign of IDPAR is negative, SPFIT constrains the ratio of this parameter to the previous parameter to a fixed value during the fit. | where IDPAR is a parameter identifier, PAR is the parameter value, ERRPAR is the parameter uncertainty, LABEL is a parameter label (10 characters are used) that is delimited by **/. ** If the sign of IDPAR is negative, SPFIT constrains the ratio of this parameter to the previous parameter to a fixed value during the fit. | ||

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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. | ||

- | ==== Format of the ''int'' File ==== | + | ===== Format of the ''int'' File ===== |

**line 1:** title | **line 1:** title | ||

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**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 //b//-dipole operator is multiplied by cos ( 3p K<sub>avg</sub>r / 3) instead of cos (4p K<sub>avg</sub>r / 3). If the magnitude of r is not the same for the two states, replace K<sub>avg</sub>r with (K<sub>1</sub>r<sub>1</sub> + K<sub>2</sub>r<sub>2</sub>) / 2. ITYP = 8 (with I1 > 0) dipoles are multiplied by //i//, and the symmetry of the states connected is 3 – SYM and the units follow the state symmetry (e.g. 81000 is in Debye ). ITYP = 2, 5 are used for first-order Herman-Wallis corrections. ITYP = 3, 4, 6, 11, 12 are used for second-order Herman-Wallis corrections. | **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 //b//-dipole operator is multiplied by cos ( 3p K<sub>avg</sub>r / 3) instead of cos (4p K<sub>avg</sub>r / 3). If the magnitude of r is not the same for the two states, replace K<sub>avg</sub>r with (K<sub>1</sub>r<sub>1</sub> + K<sub>2</sub>r<sub>2</sub>) / 2. ITYP = 8 (with I1 > 0) dipoles are multiplied by //i//, and the symmetry of the states connected is 3 – SYM and the units follow the state symmetry (e.g. 81000 is in Debye ). ITYP = 2, 5 are used for first-order Herman-Wallis corrections. ITYP = 3, 4, 6, 11, 12 are used for second-order Herman-Wallis corrections. | ||

</alert> | </alert> | ||

- | ==== Format of the ''cat'' File ==== | + | |

+ | ===== Format of the ''cat'' File ===== | ||

**[F13.4, 2F8.4, I2, F10.4, I3, I7, I4, 12I2]:** FREQ, ERR, LGINT, DR, ELO, GUP, TAG, QNFMT, QN | **[F13.4, 2F8.4, I2, F10.4, I3, I7, I4, 12I2]:** FREQ, ERR, LGINT, DR, ELO, GUP, TAG, QNFMT, QN | ||

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> QN(12) = Quantum numbers coded according to QNFMT. Upper state quanta start in character 1. Lower state quanta start in character 14. Unused quanta are blank, quanta whose magnitude is larger than 99 or smaller than –9 are shown with alphabetic characters or %%**%%. Quanta between –10 and –19 are shown as a0 through a9. Similarly, –20 is b0, etc., up to –259, which is shown as z9. Quanta between 100 and 109 are shown as A0 through A9. Similarly, 110 is B0, etc., up to 359, which is shown as Z9. | > QN(12) = Quantum numbers coded according to QNFMT. Upper state quanta start in character 1. Lower state quanta start in character 14. Unused quanta are blank, quanta whose magnitude is larger than 99 or smaller than –9 are shown with alphabetic characters or %%**%%. Quanta between –10 and –19 are shown as a0 through a9. Similarly, –20 is b0, etc., up to –259, which is shown as z9. Quanta between 100 and 109 are shown as A0 through A9. Similarly, 110 is B0, etc., up to 359, which is shown as Z9. | ||

- | ==== Format of the ''str'' File ==== | + | ===== Format of the ''str'' File ===== |

**[F15.4, E15.6, I5, 1X, 24A, I5]:** FREQ, DIPOLE, QNFMT, QN, ITEM | **[F15.4, E15.6, I5, 1X, 24A, I5]:** FREQ, DIPOLE, QNFMT, QN, ITEM | ||

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> ITEM = identifies number of dipole | > ITEM = identifies number of dipole | ||

- | ==== Format of the ''egy'' File ==== | + | ===== Format of the ''egy'' File ===== |

**energy output [2I5, 3F18.6, 6I3]:** IBLK, INDX, EGY, PMIX, ERR, QN | **energy output [2I5, 3F18.6, 6I3]:** IBLK, INDX, EGY, PMIX, ERR, QN | ||

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> QN(6) = Quantum numbers for the state | > QN(6) = Quantum numbers for the state | ||

- | ===== Special Considerations for Linear Molecules ===== | + | ====== Special Considerations for Linear Molecules ====== |

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<sub>a</sub> in the asymmetric rotor becomes lambda for the linear molecule. N is the sum of rotational and electronic orbital angular momenta. For linear molecules, it is convenient (but not essential) to think of the angular momentum along the bond as being purely electronic in nature. In the asymmetric rotor language of this program, the first-order spin orbit interaction takes the operator form of a vector dot product of a direction cosine with the spin vector. It can have two distinct symmetries: S·f<sub>a</sub> connects states of the same lambda, while S·f<sub>b</sub> and S·f<sub>c</sub> conect states where lambda differs by one. For S·f<sub>b</sub> or S·f<sub>c</sub> , the L<sub>b</sub> or L<sub>c</sub> operator is implicitly included in the parameter. When the spin orbit operator connects different spin multiplicity, the reduced matrix value of <S||**S**||S'> is set to unity. | 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<sub>a</sub> in the asymmetric rotor becomes lambda for the linear molecule. N is the sum of rotational and electronic orbital angular momenta. For linear molecules, it is convenient (but not essential) to think of the angular momentum along the bond as being purely electronic in nature. In the asymmetric rotor language of this program, the first-order spin orbit interaction takes the operator form of a vector dot product of a direction cosine with the spin vector. It can have two distinct symmetries: S·f<sub>a</sub> connects states of the same lambda, while S·f<sub>b</sub> and S·f<sub>c</sub> conect states where lambda differs by one. For S·f<sub>b</sub> or S·f<sub>c</sub> , the L<sub>b</sub> or L<sub>c</sub> operator is implicitly included in the parameter. When the spin orbit operator connects different spin multiplicity, the reduced matrix value of <S||**S**||S'> is set to unity. | ||

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The extra factors of S in the definition of the spin-spin interaction parameter l, i. e. a spin-spin interaction 2 l ( S<sub>z</sub><sup>2</sup> – S <sup>2</sup> / 3), is a correction for the special normalization assumed for eQq. | The extra factors of S in the definition of the spin-spin interaction parameter l, i. e. a spin-spin interaction 2 l ( S<sub>z</sub><sup>2</sup> – S <sup>2</sup> / 3), is a correction for the special normalization assumed for eQq. | ||

- | ===== Special Considerations for 'l'-doubled States ===== | + | ====== Special Considerations for 'l'-doubled States ====== |

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 //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.// | ||

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specifies c<sub>aa</sub> = 100, c<sub>cc</sub> = 50, and c<sub>bb</sub> = –150. | specifies c<sub>aa</sub> = 100, c<sub>cc</sub> = 50, and c<sub>bb</sub> = –150. | ||

- | ===== 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 |