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Compur. Chem. Vol, 12, No. 2, pp. 171-174,1988 Printedin GreatBritain
0097-8485/88 $3.00+0.00
Pergamon Press plc
FRANCK-CONDON V.
M.
MISKOWSKI’,
M.
ANALYSES
ON THE IBM PC/AT
M. D. HOPKINS’, D. E. BRINZA’ and H. B.
ALBIN **,
GRAY*
‘Chemical and Mechanical Systems Division, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 and *California Institute of Technology, Pasadena, CA 91125, U.S.A.
(Received
25 April
1987)
Ahstrati-A program for the rapid calculation of electronic absorption and emission spectra has been developed. The program is designed to run on the IBM PC series of computers with maximal flexibility. Sample calculations are provided for several spectra to demonstrate the utility of the software. Extensive graphic options are also provided.
This paper describes a program (3PCT”) designed for the IBM personal computers (particularly the
PC/AT). Tts purpose is to perform Franck-Condon (absorption or emission) calculations with a variety of user options. The program also has extensive graphic routines associated with it (both on-screen spectra in the paper were and hard-copy output-the * To whom correspondence
should be addressed.
all generated from the program and used as is). Details of the program, options available, system requirements, sample data and some theoretical background are given in the text below. The compiled BASIC version (1.0 or 2.0) is available from the authors; suggestions for changes and requests for the original source code will be handled on an individual basis. Figure 1 shows the configuration of the program in
Fig. 1. Flow chart illustrating options in “SPCT”. See text for details. 171
172
V. M. MISKOWSKIet al.
Xlnml
Fig. 2. Polarized single-crystalspectra (experimental} of Ru,(&CC,H,)Cl at 15K. [Reprinted from Miskowski er al. (1987) with permission from the A.C.S.]
flow chart form. Basically, the program is divided into three sections: l-generation of the line spectrum (with a maximum of three vibrational modes and any number of electronic origins). The parameters may be changed when the spectrum is displayed, before going to the next step. 2-Calculation of a line shape and summing over till the lines to generate the entire spectrum. In this step the Gaussian width, Lorentzian width and number of line widths that the line shape is calculated over are entered. Additionally, the user may change the x-axis (frequency) to expand any part, or change to a wavelength scale. 3-At this point the user may list the results to any printer, change the parameters (back to step 2), restart, or generate a publication quality figure (see Figs 3-6) on an HP7470 series plotter. This final choice will again allow the user to change many parameters (scaling, labels, etc.). All of
these options are presented in a user friendly mode on the monitor. To use the system to its maximal capability, one requires: -an IBM PC/AT with the 8087 math coprocessor; -a minimum of 512K RAM; -version 1.0 or 2.0 of the BASIC compiler; -any parallel printer; -a plotter (preferably of the HP7470 series). The program will also run on a PC/XT, but at a slower rate. The program is simply adapted to generate the spectrum as an (x,_Y) data file that can be used with other output (plotting) routines. In this section some background material on the spectral calculations will be provided, along with an example. This will include sample output at each step of the program. The methods involved in calculating
Franck-Condon 10.000
173
apalyses
r
2000
850
950
Wavelength
1050
1 1150
-
:50
Fig. 3. Calculated “stick” spectrum; vibrational/electronic parameters as in Fig. 4. electronic absorption and emission spectra within the Franck-Condon approximation are well established (Ballhausen, 1979). Transition moments relative to the electronic origin (usually represented by the (l-O)/(@O) ratio, S, the Huang-Rhys ratio*) can be easily calculated via recursion formulas and corrections [e.g. the “Einstein” frequency dependence of transition probability, Yersin ef al. (1980)] applied. The latter correction is automatically applied to line-shape spectra in this program. The program then convolutes the “stick” spectrum with an appropriate line-shape function to produce the final simulated spectrum. The line-shape function may be Gaussian, Lorentzian or a specified mixture of both (calculated by published algorithms) (BelBruno et al., 1981; Hui er al., 1978). For each of the vibrational modes (e.g. progression forming modes), we allow for different initial and final state frequencies. Therefore, except for mode-mixing (Ballhausen, 1979), we achieve maximal accuracy possible within the Franck-Condon approximation. The program allows for only three active vibrational modes as a larger number would stretch the limits (ordinarily memory) of what is most commonly available. We allow for a large number of electronic origins. In practice, we have found that a Franck-Condon active vibration may be treated as an electronic origin if S is small (10.2) since progressions in it are then exceedingly weak.
950
1050
Wavelength
h-irn~
4150
(nm)
Fig. 4. Calculated n spectrum (Fir. 2): parameters: vi&rational frequencies _ (initial, . f&al, ‘. kuang-Rhys factor) = 330,308,0.7; 432,432,O.z 695,695,0.l/electronic origin = 8897 cm-‘/six Lorentzian widths of 60 cm-‘.
axis; while the u and a spectra are for radiation polarized perpendicular to Ru,. The data have been interpreted (Miskowski et al., 1987). Calculated spectra are shown in Figs 3-4 (parameters are given in the figure captions). Figure 3 shows the “stick” spectrum that is generated in the
first part of the program
for
the x spectrum.
This
(Fig. 4) is interpreted as an allowed electronic transition with three progressional modes. In Fig. 5, we slightly improve upon the calculated spectrum (of Fig. 4) by accounting for a weak side band as an extra electronic origin. The extra “origin” is probably a lattice mode. In Fig. 6 we simulate the (T and Q spectra. Three spectrum
Sample calculation Figure 2 shows the electronic absorption spectra for the compound Ru,(02C-C,H7)CI, which adopts a tetragonal structure with (RuzCI), chains parallel to the crystal c axis (Miskowski et al., 1987). The n spectrum is for radiation polarized parallel to the Ru2 * The parameter S is related to molecular bond distortions (see BaMhausen, 1979).
Wavetength
(nm)
Fig. 5. Calculated x spectrum (as Fig. 4) with one additional electronic origin at 9OOOcm-’ (0.10 relative intensity to 8897 HIT-’ origin). The effect is evident in several peaks-that now exhibit weak shoulders.
V. M. MI~KOWSKI et al.
174
electronic origin at 8897cm-’ is added, it results solely due to slight crystal misorientation. Note that the value of S needed for the 330/308cm-’ mode is different from that required to fit the n: spectrum. This is an example of a vibronic coupling effect (Miskowski et al., 1987).
10,000
a000
21 ,s 5 = u
6000 Acknowledgemenrs-This research was supported by the National Science Foundation Grants CHE 84-19828 and CHE 8518793. Part of the research described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The authors gratefully acknowledge work by Colin J. P. Tilcock on parts of the HP7470A driver portion of the program.
4000
2000
E
,
I 950
I 1050
u 1150
Wavelengthf nm 1 Fig. 6. Calculated IJand a spectrum; parameters; vibrational frequencies (initial, final, S) = 330,30&I; 432,432,0.2; 695,695,O. 1/electronic origins (cm-‘), intensities = 8897.0.2; 9130.0.7: 9207.1 .O: 10342, LO/sin Lorentzian widths of 70 cm-‘. vibronic and three electronic origins are assumed to generate a reasonable fit. A small amount of the
REFERENCES Ballhausen C. J. (1979) Molecular Electronic Structures of Transition Metal Complexes, Chap. 4. McGraw-Hi& New York. Belbruno J. J., Zughul M. B., Gelfand J. & Rabitz H. (1981) J. Mol. Spectrosc. 87, 560. Hui A. K., Armstrong B. H. & Wray A. A. (1978) J. Quant. Spectrosc. Rudiut. Transfer 19, 509. Miskowski V. M., Loehr T. M. & Gray H. B. (1987) Jnorg. Ckm. 26, 1098. Yersin H., Oho H., Zink J. I. & Gliemann G. (1980) J. Am. Gem. Sot. 102, 951.
0097-8485/88 $3.00+0.00
Pergamon Press plc
FRANCK-CONDON V.
M.
MISKOWSKI’,
M.
ANALYSES
ON THE IBM PC/AT
M. D. HOPKINS’, D. E. BRINZA’ and H. B.
ALBIN **,
GRAY*
‘Chemical and Mechanical Systems Division, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 and *California Institute of Technology, Pasadena, CA 91125, U.S.A.
(Received
25 April
1987)
Ahstrati-A program for the rapid calculation of electronic absorption and emission spectra has been developed. The program is designed to run on the IBM PC series of computers with maximal flexibility. Sample calculations are provided for several spectra to demonstrate the utility of the software. Extensive graphic options are also provided.
This paper describes a program (3PCT”) designed for the IBM personal computers (particularly the
PC/AT). Tts purpose is to perform Franck-Condon (absorption or emission) calculations with a variety of user options. The program also has extensive graphic routines associated with it (both on-screen spectra in the paper were and hard-copy output-the * To whom correspondence
should be addressed.
all generated from the program and used as is). Details of the program, options available, system requirements, sample data and some theoretical background are given in the text below. The compiled BASIC version (1.0 or 2.0) is available from the authors; suggestions for changes and requests for the original source code will be handled on an individual basis. Figure 1 shows the configuration of the program in
Fig. 1. Flow chart illustrating options in “SPCT”. See text for details. 171
172
V. M. MISKOWSKIet al.
Xlnml
Fig. 2. Polarized single-crystalspectra (experimental} of Ru,(&CC,H,)Cl at 15K. [Reprinted from Miskowski er al. (1987) with permission from the A.C.S.]
flow chart form. Basically, the program is divided into three sections: l-generation of the line spectrum (with a maximum of three vibrational modes and any number of electronic origins). The parameters may be changed when the spectrum is displayed, before going to the next step. 2-Calculation of a line shape and summing over till the lines to generate the entire spectrum. In this step the Gaussian width, Lorentzian width and number of line widths that the line shape is calculated over are entered. Additionally, the user may change the x-axis (frequency) to expand any part, or change to a wavelength scale. 3-At this point the user may list the results to any printer, change the parameters (back to step 2), restart, or generate a publication quality figure (see Figs 3-6) on an HP7470 series plotter. This final choice will again allow the user to change many parameters (scaling, labels, etc.). All of
these options are presented in a user friendly mode on the monitor. To use the system to its maximal capability, one requires: -an IBM PC/AT with the 8087 math coprocessor; -a minimum of 512K RAM; -version 1.0 or 2.0 of the BASIC compiler; -any parallel printer; -a plotter (preferably of the HP7470 series). The program will also run on a PC/XT, but at a slower rate. The program is simply adapted to generate the spectrum as an (x,_Y) data file that can be used with other output (plotting) routines. In this section some background material on the spectral calculations will be provided, along with an example. This will include sample output at each step of the program. The methods involved in calculating
Franck-Condon 10.000
173
apalyses
r
2000
850
950
Wavelength
1050
1 1150
-
:50
Fig. 3. Calculated “stick” spectrum; vibrational/electronic parameters as in Fig. 4. electronic absorption and emission spectra within the Franck-Condon approximation are well established (Ballhausen, 1979). Transition moments relative to the electronic origin (usually represented by the (l-O)/(@O) ratio, S, the Huang-Rhys ratio*) can be easily calculated via recursion formulas and corrections [e.g. the “Einstein” frequency dependence of transition probability, Yersin ef al. (1980)] applied. The latter correction is automatically applied to line-shape spectra in this program. The program then convolutes the “stick” spectrum with an appropriate line-shape function to produce the final simulated spectrum. The line-shape function may be Gaussian, Lorentzian or a specified mixture of both (calculated by published algorithms) (BelBruno et al., 1981; Hui er al., 1978). For each of the vibrational modes (e.g. progression forming modes), we allow for different initial and final state frequencies. Therefore, except for mode-mixing (Ballhausen, 1979), we achieve maximal accuracy possible within the Franck-Condon approximation. The program allows for only three active vibrational modes as a larger number would stretch the limits (ordinarily memory) of what is most commonly available. We allow for a large number of electronic origins. In practice, we have found that a Franck-Condon active vibration may be treated as an electronic origin if S is small (10.2) since progressions in it are then exceedingly weak.
950
1050
Wavelength
h-irn~
4150
(nm)
Fig. 4. Calculated n spectrum (Fir. 2): parameters: vi&rational frequencies _ (initial, . f&al, ‘. kuang-Rhys factor) = 330,308,0.7; 432,432,O.z 695,695,0.l/electronic origin = 8897 cm-‘/six Lorentzian widths of 60 cm-‘.
axis; while the u and a spectra are for radiation polarized perpendicular to Ru,. The data have been interpreted (Miskowski et al., 1987). Calculated spectra are shown in Figs 3-4 (parameters are given in the figure captions). Figure 3 shows the “stick” spectrum that is generated in the
first part of the program
for
the x spectrum.
This
(Fig. 4) is interpreted as an allowed electronic transition with three progressional modes. In Fig. 5, we slightly improve upon the calculated spectrum (of Fig. 4) by accounting for a weak side band as an extra electronic origin. The extra “origin” is probably a lattice mode. In Fig. 6 we simulate the (T and Q spectra. Three spectrum
Sample calculation Figure 2 shows the electronic absorption spectra for the compound Ru,(02C-C,H7)CI, which adopts a tetragonal structure with (RuzCI), chains parallel to the crystal c axis (Miskowski et al., 1987). The n spectrum is for radiation polarized parallel to the Ru2 * The parameter S is related to molecular bond distortions (see BaMhausen, 1979).
Wavetength
(nm)
Fig. 5. Calculated x spectrum (as Fig. 4) with one additional electronic origin at 9OOOcm-’ (0.10 relative intensity to 8897 HIT-’ origin). The effect is evident in several peaks-that now exhibit weak shoulders.
V. M. MI~KOWSKI et al.
174
electronic origin at 8897cm-’ is added, it results solely due to slight crystal misorientation. Note that the value of S needed for the 330/308cm-’ mode is different from that required to fit the n: spectrum. This is an example of a vibronic coupling effect (Miskowski et al., 1987).
10,000
a000
21 ,s 5 = u
6000 Acknowledgemenrs-This research was supported by the National Science Foundation Grants CHE 84-19828 and CHE 8518793. Part of the research described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The authors gratefully acknowledge work by Colin J. P. Tilcock on parts of the HP7470A driver portion of the program.
4000
2000
E
,
I 950
I 1050
u 1150
Wavelengthf nm 1 Fig. 6. Calculated IJand a spectrum; parameters; vibrational frequencies (initial, final, S) = 330,30&I; 432,432,0.2; 695,695,O. 1/electronic origins (cm-‘), intensities = 8897.0.2; 9130.0.7: 9207.1 .O: 10342, LO/sin Lorentzian widths of 70 cm-‘. vibronic and three electronic origins are assumed to generate a reasonable fit. A small amount of the
REFERENCES Ballhausen C. J. (1979) Molecular Electronic Structures of Transition Metal Complexes, Chap. 4. McGraw-Hi& New York. Belbruno J. J., Zughul M. B., Gelfand J. & Rabitz H. (1981) J. Mol. Spectrosc. 87, 560. Hui A. K., Armstrong B. H. & Wray A. A. (1978) J. Quant. Spectrosc. Rudiut. Transfer 19, 509. Miskowski V. M., Loehr T. M. & Gray H. B. (1987) Jnorg. Ckm. 26, 1098. Yersin H., Oho H., Zink J. I. & Gliemann G. (1980) J. Am. Gem. Sot. 102, 951.