DIATOM Spectral Simulation Program

• Introduction
• DIATOM Command Verbs
• External Data Files
  • Spectroscopic Constants
  • Franck-Condon Factors
  • Transition Moment Matrix
• KVS Command Processor
• Reference Publications
• Related Web Pages

Spectroscopic parameters for the upper and lower electronic states are read from user-specified data files. Vibrational band strengths are specified by an electronic transition dipole moment and a Franck-Condon Factor data file (possibly implicitly representing dependence of the transition moment on v' and v"), and optionally multiplied by a user-specified population fraction. Rotational branch strengths are calculated from eigenvectors of the rotation-fine-structure hamiltonians for the upper and lower vibronic levels (Hönl-London Factors) and relative populations (Boltzmann Factors).

Many types of "forbidden" transitions are treated, including spin-orbit and rotational "borrowing" of transition strength, often recognized automatically, including magnetic-dipole transitions in homonuclear molecules. The details can be specified by a "rotated" transition moment or an explicit transition-moment-matrix data file. The electronic structure of the upper and lower states can be specified quite generally, even including singlet-triplet spin-complexes and sigma-pi L-complexes.

DIATOM activites are controlled by KVS commands. Those that are specifie to DIATOM are described below. Others, i.e. those beginning with periods, are described in separate documentaion of the KVS command processor. You are likely to benefit from experience with the GRA interactive graph manipulation program.

The following describes the basic steps.

1. Use a text file editor to create a KVS script file.

   UPPER upper-state-constants-file
   LOWER lower-state-constants-file
   FCF Franck-Condon-Factor-file
   TEMP -1/rotational-temperature
   WAVENUMBER wn-low,wn-high
   ONLYV v-upper,v-lower
   BROAD
   GRASP
   

2. Invoke the DIATOM application with a script file

   DIATOM .lgo KVS-script-file

3. Alternatively, invoke DIATOM for interactive execution

   DIATOM

• CLRSP
  Zeroes the accumulated spectrum.

• BROAD
  Calculates a "broadened" synthetic spectrum and adds it to the accumulated sum.

• DISSOCIATION De-upper De-lower
  Supplies optional dissociation limits for the upper and lower states. Any rotational levels above the corresponding dissociation limit are ignored.

• EMISSION
  Indicates that an emission spectrum is to be calculated, with intensities corresponding to calculated excited state populations. Note that it is actually the stimulated emission cross section spectrum that is calculated rather than the fluorescence intensity spectrum. Once specified, EMISSION remains in effect until DIATOM exits.

• FCF file-specification [/LIST]
  Reads a file of Franck-Condon factors. If no file .extension is specified, .FCF is used by default. Entering the /LIST option will cause a summary of the data to be listed on the screen.

• FRACTION floating-number
  Indicates the factor by which to multiply future calculated spectra before adding them to the accumulated sum.

• GRASP [/option]
  Graphs the current accumulated spectrum. If you enter /NM the x-axis is vacuum wavelength. If you enter /AIR the x-axis is air wavelength. Use the WAVELENGTH command to set the limits. If neither option is provided, the spectrum is graphed versus wavenumber (cm^-1). Use the SPMAX command to control the y-axis limits.

• HOMONUCLEAR nuclear-spin
  HOMONUCLEAR symmetric-factor antisymmetric-factor
  Controls the nuclear spin statistics for a homonuclear diatomic molecule. You can explicitly enter the relative amplitudes, or you can let DIATOM calculate them from the value of the nuclear spin.

• LINES [ max-J ] [ ordered-by ]
  Lists the line positions for a limited range of J values ordered by J, N, Branch, or Energy (ordered-by = J, N, B, or E respectively). A specific vibrational transition must have been specified already with the ONLYV command. To record the line positions in a file, use the following three steps:

  DIATOM> .TRACE LINES 2
  DIATOM> LINES max-J ordered-by
  DIATOM> .TRACE/6

  When DIATOM exits it will have written a file named FOR002.DAT containing the term energies. Multiple .TRACE commands in the same execution session may get written to the same file. You can also use the KVS .F77 create() and close() actions to control .TRACE files.

• LOWER file-specification [/LIST]
  Reads spectroscopic information about the lower state. If no file extension is specified, .CON (spectroscopic CONstants) is tried first, followed by .DUN (DUNham coefficients). Entering the /LIST option will cause a summary of the data to be listed on the screen.

• ONLYV v-upper v-lower
  Selects the vibrational levels to be included in the spectrum. A negative number indicates that all vibrational levels of the electronic state are to be included. A non-negative number selects a specific vibrational level.

• REFMASS mass-1 mass-2
  REFMASS reduced-mass
  Supplies the masses that are appropriate for the Dunham coefficients that are about to be read with LOWER or UPPER.

• SAVESP file-specification
  Saves a copy of the accumulated spectrum in the file provided.

• SHIFT number LOWER
  SHIFT number UPPER
  Adds the number given to all the vibrational energy levels of the state indicated.

• SPMASS mass-1 mass-2
  SPMASS reduced-mass
  Supplies the masses to which the Dunham coefficients (that are about to be read with LOWER or UPPER) should be scaled.

• SPMAX floating-number
  Indicates the upper limit of the y-axis of a graph. Note that the units of SPMAX are cm², while the y-axis label says megabarns (1MB = 1.E-18 cm²) so that you have to enter something of the form yyy.zzzE-18

• TEMP T-vib T-rot
  Indicates the temperature (in K) to be used when calculating populations (Boltzmann factors). At present only the rotational temperature is used correctly. Always enter T-vib as -1.

• TERMS max-J LOWER
  TERMS max-J UPPER
  Lists the term energies for a limited range of J values for the electronic state indicated. A specific vibrational level must have been specified in advance with the ONLYV command. To record the term energies in a file, use the following three steps:

  DIATOM> .TRACE TERMS 2
  DIATOM> TERMS max-J upper-or-lower
  DIATOM> .TRACE/6

  When DIATOM exits it will have written a file named FOR002.DAT containing the term energies. Multiple .TRACE commands in the same execution session may get written to the same file. You can also use the KVS .F77 create() and close() actions to control .TRACE files.

• TRANSMOMENT mu theta [file-specification]
  Indicates the value of the electronic transition moment (in Debye), a rotation angle by which it is to be rotated away from the expected parallel or perpendicular direction, and an optional file containing an explicit transition moment matrix over fine structure components.

• UPPER file-specification [/LIST]
  Reads spectroscopic information about the upper state. If no file extension is specified .CON (spectroscopic CONstants) is tried first, followed by .DUN (DUNham coefficients). Entering the /LIST option will display a summary of the data to be listed on the screen.

• WAVELENGTH wl-low wl-high
  Provides optional limits (in nm) for a graph of a spectrum with wavelength along the x-axis.

• WAVENUMBER wn-low wn-high
  Supplies required limits for the spectrum to be calculated, in units of cm^-1. The spectrum is calculated at up to 2000 equally spaced points, depending on the values specified in the WIDTH command. If you enter WAVENUMBER for a second time, the previously accumulated spectrum is zeroed.

• WIDTH wn-width [/line-shape-code]
  WIDTH wl-width /negative-line-shape-code
  Specifies the full-width-at-half-maximum of the calculated rotational lines. The line-shape-code selects a line shape function (a negative value indicates units of nm, otherwise the units are cm^-1):
  1. triangles (the default),
  2. rectanges
  3. gaussian
  4. lorentzian

If a file name.CON is read, the spectroscopic parameters or "constants" are specified directly as term energies (G_v), rotational constants (B_v, D_v, etc.), and fine structure constants for each individual vibrational level.

If a file name.DUN is read, the spectroscopic constants for the individual levels are calculated from polynomial expressions using the Dunham coefficients T_e, omega_e, -omega_ex_e, B_e, -alpha_e, etc., including vibrational representation of the fine structure constants. Expression of the Dunham coefficients is modified by previously entered REFMASS and SPMASS commands.

• name.CON
  1. READ 2, T0,MXV,NJC,NF,LAMBDA,IPARITY,SPIN,OMEGA,DELTA
  2. FORMAT(F20.0,5I5,3F20.0)

  3. DO 4 I=0,MXV
  4. READ 5, GV(I),(ROTV(J,I),J=1,NJC),(FINEV(K,I),K=1,NF)
  5. FORMAT(5F20.0)

• name.DUN
  1. READ 2, NV,NJ,LAMBDA,IPARITY,SPIN,OMEGA,DELTA,NF,NVF
  2. FORMAT(4I5,3F15.0,2I5)

  3. DO 4 I=1,NV
  4. READ 5, (Y(I,K),K=1,NJ)
  5. FORMAT(5F20.0)

  6. DO 7 I=1,NVF
  7. READ 8, (FINE(I,J),J=1,NF)
  8. FORMAT(5F20.0)

• DELTA is reserved for future use

• FINE(I,J) are the fine-structure Dunham coefficients

  FINEV(J,v) = sum-over(i=1,...) FINE(i,J)*(v+0.5)^(i-1)

• FINEV(K,v) are the fine-structure constants:

  FINEV(1,v) = A_v (spin-orbit)
  FINEV(2,v) = lambda_v (spin-spin)
  FINEV(3,v) = gamma_v (spin-rotation)
  FINEV(4,v) = A_Dv (CD of spin orbit)
  FINEV(5,v) = lambda_Dv (CD of spin-spin)
  FINEV(6,v) = gamma_Dv (CD of spin-rotation)
  FINEV(7,v) = q_v (lambda-doubling)
  FINEV(8,v) = p_v (lambda-doubling)
  FINEV(9,v) = o_v (lambda-doubling)
  FINEV(10,v) = eta_v (sigma splitting)
  FINEV(11,v) = K (singlet-triplet splitting)
  FINEV(12,v) = (sigma-pi splitting)

• GV(v) are the vibrational term energies

• IPARITY is the parity indicator
  bit-0 = 1 indicates Sigma^- (Sigma-minus)
  bit-1 = 1 indicates ungerade

  IPARITY = 0 for Sigma_g⁺, Pi_g, Delta_g etc
  IPARITY = 1 for Sigma_g^-
  IPARITY = 2 for Sigma_u⁺, Pi_u, Delta_u etc
  IPARITY = 3 for Sigma_u^-

• LAMBDA is the orbital angular momentum projection LAMBDA. If LAMBDA < 0 a L-complex is generated with L = |LAMBDA|

• MXV (<99) is the number of the highest vibrational level

• NJ is the number of rotational terms in the Dunham expansion

• NJC (<6) is the number of rotational constants

• NF (<16) is the number of fine-structure constants

• NV is the number of vibrational terms in the Dunham expansion

• NVF is the number of vibrational terms in the Dunham expansion of the fine-structure constants

• OMEGA
  is the total angular momentum projection. If SPIN > 0 and OMEGA .ne. 0 then Hund's case (c) coupling is used (considering only the given value of OMEGA) rather than intermediate coupling (in which all possible values of OMEGA are included).

• ROTV(J,v) are the rotational constants Bv, Dv, Hv, Lv, Mv

• SPIN is the electron spin (0,0.5,1, etc). If SPIN < 0, a spin- complex is generated: |SPIN|, |SPIN|-1, ...

• T0 is an optional offset to be added to the vibrational energies.

• Y(I,K) are the Dunham coefficients

  GV(v) = sum-over(i=1,...) Y(i,1)*(v+0.5)^(i-1), v=0,...

  ROTV(J,v) = (-1)^(J+1) sum-over(i=1,...) Y(i,J+1)*(v+0.5)^(i-1), J=1,..., v=0,...

• Return to Main Menu
• Return to LOWER command
• Return to UPPER command
• Return to REFMASS command
• Return to SPMASS command

Franck-Condon factors are read from a file name.FCF in the format

1. READ 2, TITLE
2. FORMAT(10A8)

3. READ 4, MXVU, MXVL
4. FORMAT(2I5)

5. DO 6 IU=0,MXVU
6. READ 7, (FCF(IU,IL),IL=0,MXVL)
7. FORMAT(10F8.3)

• TITLE is user information (source reference etc.)

• MXVU,MXVL highest vibrational levels in upper and lower states

• FCF(IU,IL) is the squared Franck-Condon factor
  

  Reasonable choices for the format are:
  1.234-1,9.876-1, etc
  123,988, etc

  Note that the comma must be within the eight character field, and that a three-digit number without a decimal point will be divided by 1000.

• Return to Main Menu
• Return to FCF command

The optional transition moment matrix for forbidden transitions is read from a file name.TRA or name.TRANS in the format

1. DO 2 KBFU=1,NBFU
2. READ *,(TRANS(KBFU,KBFL),KBFL=1,NBFL)

3. DO 4 KBFU=1,NBFU
4. READ *,(RTPLUS(KBFU,KBFL),KBFL=1,NBFL)

5. DO 6 KBFU=1,NBFU
6. READ *,(RTMINUS(KBFU,KBFL),KBFL=1,NBFL)

DIATOM defines the basis functions |SPIN,LAMBDA,SIGMA> in the order of

1. increasing SPIN
2. increasing LAMBDA
3. increasing SIGMA

• Return to Main Menu
• Return to TRANSMOMENT command

• KVS Manual (local version of KVS.html, e.g. if downloaded to your hard drive, or KVS.htm alternative)
• KVS Manual (latest version on MPL server)

• Return to DIATOM Main Menu

• D. L. Huestis, "Radiative Transition Probabilities," in Atomic, Molecular, and Optical Physics Handbook, G.W.F. Drake, Ed. (AIP Press, Woodbury, NY, 1996).

• Return to DIATOM Main Menu

• Molecular Physics Laboratory Home Page
• SRI International Home Page

• Return to DIATOM Main Menu
• Download DIATOM executable

Send comments and suggestions to david.huestis@sri.com

URL: http://www-mpl.sri.com/manuals/DIATOM.html