Franck-Condon Factors for A<-X in CO ================================================================================ Generate ZMU= 6.85620863850(u) & BZ= 4.067125102E-01((1/cm-1)(1/Ang**2)) from atomic masses: 12.0000000000 & 15.9949146223(u) Integrate from RMIN= 0.500 to RMAX= 30.50 with mesh RH= 0.001500(Angst) Potential #1 for C( 12)- O( 16) ================================ Absolute energy at asymptote: Y(lim)= 89462.1900(cm-1) Perform 8-point piecewise polynomial interpolation over 130 input points Interpolation performed over modified input array: Y(I) * R(I)**2 Scale input points: (distance)* 1.000000000E+00 & (energy)* 1.000000000E+00 to get required internal units [Angstroms & cm-1 for potentials] R(i) Y(i) R(i) Y(i) R(i) Y(i) ---------------------- ---------------------- ---------------------- 0.88830000 33945.6574 1.07358935 8233.5372 1.46513511 7546.3360 0.90350000 31273.5363 1.07693403 7890.3591 1.47128625 7890.3591 0.91870000 28720.6762 1.08034192 7546.3360 1.47729080 8233.5372 0.93390000 26281.7542 1.08381931 7201.3959 1.48315343 8575.9419 0.94910000 23951.6851 1.08737334 6855.4670 1.48887820 8917.6451 0.96431262 21723.8041 1.09101223 6508.4776 1.49446867 9258.7186 0.96688126 21357.5722 1.09474537 6160.3559 1.49992795 9599.2343 0.96945600 20993.2959 1.09858370 5811.0299 1.50525880 9939.2639 0.97203705 20630.9033 1.10253996 5460.4279 1.51046363 10278.8792 0.97462467 20270.3226 1.10662916 5108.4781 1.51554459 10618.1521 0.97721908 19911.4821 1.11086918 4755.1087 1.52050359 10957.1544 0.97982057 19554.3099 1.11528151 4400.2479 1.52534232 11295.9579 0.98242942 19198.7342 1.11989241 4043.8238 1.53006231 11634.6344 0.98504594 18844.6831 1.12473443 3685.7646 1.53466491 11973.2556 0.98767045 18492.0850 1.12984868 3325.9986 1.53915136 12311.8935 0.99030330 18140.8679 1.13528835 2964.4539 1.54352278 12650.6199 0.99294487 17790.9600 1.14112421 2601.0587 1.54778018 12989.5065 0.99559556 17442.2896 1.14745383 2235.7411 1.55192449 13328.6251 0.99825581 17094.7849 1.15441825 1868.4295 1.55595659 13668.0477 1.00092608 16748.3739 1.16223478 1499.0519 1.55987726 14007.8459 1.00360688 16402.9849 1.17127054 1127.5365 1.56368727 14348.0916 1.00629875 16058.5461 1.18224399 753.8116 1.56738731 14688.8566 1.00900228 15714.9857 1.19701740 377.8054 1.57097808 15030.2128 1.01171809 15372.2319 1.23521413 0.0000 1.57446022 15372.2319 1.01444689 15030.2128 1.27765606 377.8054 1.57783435 15714.9857 1.01718940 14688.8566 1.29662057 753.8116 1.58110111 16058.5461 1.01994644 14348.0916 1.31172358 1127.5365 1.58426109 16402.9849 1.02271889 14007.8459 1.32482614 1499.0519 1.58731489 16748.3739 1.02550768 13668.0477 1.33664555 1868.4295 1.59026312 17094.7849 1.02831386 13328.6251 1.34754775 2235.7411 1.59310639 17442.2896 1.03113854 12989.5065 1.35774884 2601.0587 1.59584529 17790.9600 1.03398297 12650.6199 1.36738871 2964.4539 1.59848045 18140.8679 1.03684847 12311.8935 1.37656377 3325.9986 1.60101250 18492.0850 1.03973651 11973.2556 1.38534363 3685.7646 1.60344207 18844.6831 1.04264869 11634.6344 1.39378033 4043.8238 1.60576983 19198.7342 1.04558678 11295.9579 1.40191385 4400.2479 1.60799644 19554.3099 1.04855269 10957.1544 1.40977564 4755.1087 1.61012260 19911.4821 1.05154854 10618.1521 1.41739082 5108.4781 1.61214900 20270.3226 1.05457668 10278.8792 1.42477983 5460.4279 1.61407637 20630.9033 1.05763968 9939.2639 1.43195944 5811.0299 1.61590547 20993.2959 1.06074040 9599.2343 1.43894363 6160.3559 1.61763705 21357.5722 1.06388200 9258.7186 1.44574410 6508.4776 1.61927190 21723.8041 1.06706799 8917.6451 1.45237075 6855.4670 1.07030231 8575.9419 1.45883202 7201.3959 ------------------------------------------------------------------------ To make above input points consistent with Y(lim), add Y(shift)= 65075.7700 Extrapolate to X .le. 0.9035 with Y= 39150.776 +8.630641E+05 * exp(-3.003830E+00*R) Extrapolate to X .GE. 1.6176 using Y= 89462.1900 -1.350414E+30/X**( 1.275807E+02)] , yielding NCN=127 ------------------------------------------------------------------------------ Get matrix elements between levels of Potential-1 (above) & Potential-2 (below) ------------------------------------------------------------------------------ For Potential #2: ================= Absolute energy at asymptote: Y(lim)= 89462.1900(cm-1) Perform 8-point piecewise polynomial interpolation over 132 input points Interpolation performed over modified input array: Y(I) * R(I)**2 Scale input points: (distance)* 1.000000000E+00 & (energy)* 1.000000000E+00 to get required internal units [Angstroms & cm-1 for potentials] R(i) Y(i) R(i) Y(i) R(i) Y(i) ---------------------- ---------------------- ---------------------- 0.89260000 48762.7838 0.99411212 12039.2844 1.30515133 10008.1227 0.90040000 44584.7759 0.99654502 11533.9539 1.31069416 10518.3741 0.90820000 40687.4587 0.99905535 11026.9841 1.31615548 11026.9841 0.91600000 37051.9747 1.00164888 10518.3741 1.32154183 11533.9539 0.92380000 33660.7331 1.00433208 10008.1227 1.32685901 12039.2844 0.93164679 30479.0032 1.00711235 9496.2290 1.33211221 12542.9765 0.93278204 30036.8378 1.00999808 8982.6921 1.33730606 13045.0312 0.93393307 29593.0716 1.01299899 8467.5109 1.34244475 13545.4496 0.93510030 29147.7034 1.01612629 7950.6845 1.34753207 14044.2326 0.93628417 28700.7324 1.01939316 7432.2119 1.35257147 14541.3812 0.93748513 28252.1575 1.02281518 6912.0921 1.35756607 15036.8964 0.93870366 27801.9777 1.02641101 6390.3241 1.36251876 15530.7792 0.93994025 27350.1922 1.03020332 5866.9069 1.36743216 16023.0305 0.94119542 26896.7998 1.03422010 5341.8395 1.37230871 16513.6514 0.94246973 26441.7997 1.03849659 4815.1210 1.37715064 17002.6428 0.94376374 25985.1908 1.04307820 4286.7504 1.38196003 17490.0058 0.94507805 25526.9721 1.04802517 3756.7266 1.38673880 17975.7412 0.94641329 25067.1427 1.05342029 3225.0488 1.39148874 18459.8501 0.94777013 24605.7015 1.05938294 2691.7158 1.39621153 18942.3335 0.94914925 24142.6476 1.06609654 2156.7268 1.40090872 19423.1923 0.95055140 23677.9800 1.07387020 1620.0807 1.40558178 19902.4276 0.95197733 23211.6977 1.08330743 1081.7766 1.41023207 20380.0403 0.95342789 22743.7997 1.09596812 541.8135 1.41486088 20856.0314 0.95490391 22274.2851 1.12769275 0.1903 1.41946942 21330.4019 0.95640632 21803.1528 1.12832278 0.0000 1.42405884 21803.1528 0.95793608 21330.4019 1.12895376 0.1903 1.42863021 22274.2851 0.95949422 20856.0314 1.16339077 541.8135 1.43318456 22743.7997 0.96108182 20380.0403 1.17877121 1081.7766 1.43772286 23211.6977 0.96270005 19902.4276 1.19093563 1620.0807 1.44224601 23677.9800 0.96435015 19423.1923 1.20144395 2156.7268 1.44675490 24142.6476 0.96603341 18942.3335 1.21089970 2691.7158 1.45125036 24605.7015 0.96775127 18459.8501 1.21961206 3225.0488 1.45573317 25067.1427 0.96950522 17975.7412 1.22776447 3756.7266 1.46020409 25526.9721 0.97129688 17490.0058 1.23547634 4286.7504 1.46466383 25985.1908 0.97312800 17002.6428 1.24283053 4815.1210 1.46911309 26441.7997 0.97500044 16513.6514 1.24988729 5341.8395 1.47355253 26896.7998 0.97691624 16023.0305 1.25669209 5866.9069 1.47798277 27350.1922 0.97887758 15530.7792 1.26328021 6390.3241 1.48240443 27801.9777 0.98088685 15036.8964 1.26967967 6912.0921 1.48681807 28252.1575 0.98294662 14541.3812 1.27591319 7432.2119 1.49122427 28700.7324 0.98505973 14044.2326 1.28199948 7950.6845 1.49562356 29147.7034 0.98722926 13545.4496 1.28795416 8467.5109 1.50001646 29593.0716 0.98945861 13045.0312 1.29379043 8982.6921 1.50440347 30036.8378 0.99175152 12542.9765 1.29951957 9496.2290 1.50878506 30479.0032 ------------------------------------------------------------------------ To make above input points consistent with Y(lim), add Y(shift)= 0.0000 Extrapolate to X .le. 0.9004 with Y= -13425.760 +1.778591E+08 * exp(-8.916173E+00*R) Function for X .GE. 1.5044 generated as Y= 89462.1900 - ( 1.238715E+05) * exp{- 0.983869 * (R - 0.640363)**2} ------------------------------------------------------------------------------ Eigenvalue convergence criterion is EPS= 1.0E-04(cm-1) Airy function at 3-rd turning point is quasibound outer boundary condition State-1 electronic angular momentum OMEGA= 0 yields centrifugal potential [J*(J+1) - 0.00]/R**2 For J= 1, try to find the first 16 vibrational levels of Potential-1 Coefficients of expansion for radial matrix element/expectation value argument: 1.000000E+00 Using the rotational selection rule: delta(J)= -1 to-1 with increment 1 calculate matrix elements for coupling to the 1 vibrational levels of Potential-2: v = 0 State-2 electronic angular momentum OMEGA= 0 yields centrifugal potential [J*(J+1) - 0.00]/R**2 ------------------------------------------------------------------------------- Find 16 Potential-1 vibrational levels with J= 1 v E(v) v E(v) v E(v) v E(v) -------------- -------------- -------------- -------------- 0 65832.4206 4 71586.4464 8 77054.3118 12 82528.8678 1 67313.7690 5 72968.7969 9 78411.0170 13 83929.1258 2 68763.5012 6 74337.8275 10 79772.8523 14 85344.5810 3 70186.2030 7 75698.1277 11 81144.2170 15 86769.5197 ===============================================================================