Matrix Elements of P ================================================================================ 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 ------------------------------------------------------------------------------ Calculate properties of the single potential described above 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 Matrix element argument is radial first derivative operator premultiplied by a power series in R of order 0 Coefficients of expansion for radial matrix element/expectation value argument: 1.000000E+00 Using the rotational selection rule: delta(J)= 0 to 0 with increment 1 calculate matrix elements for coupling to the 16 vibrational levels of Potential-2: v = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ------------------------------------------------------------------------------- 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 ===============================================================================