! EXAM 39. ! The non-resonant Raman and hyper-Raman spectra of CH4 ! ! This run generates results similar to four published papers, ! although the basis set in this test is much smaller. This ! run (3-21G) can be run in a few seconds, making it suitable ! for a GAMESS test input, but not for publishable results. ! ! The basis set for polarizabilities should be large, and have ! appreciable diffuse character. Good choices are the Sadlej ! basis set named POL, or augmented-cc-pVDZ (GBASIS=ACCD). ! The 3-21G run takes 10 seconds on a certain computer, short ! enough to be a test case, whereas ACCD takes 1217 seconds. ! ! dAlpha/dx and dBeta/dX are computed by iterative and non- ! iterative means, to be sure that they get the same results. ! ! The log file contains the following things, in this order. ! Search on the phrase "procedure to xcompute", with no x, for ! Iterative procedure to xcompute Alpha(-0.04; 0.04) ! Iterative procedure to xcompute dAlphadX(-0.04; 0.04) ! Non-Iterative procedure to xcompute dAlphadX(-0.04; 0.04) ! Non-Iterative procedure to xcompute Mu ! Iterative procedure to xcompute Beta(-0.08; 0.04, 0.04) ! Iterative procedure to xcompute dBetadX(-0.08; 0.04, 0.04) ! Iterative procedure to xcompute Alpha( 0.08;-0.08) ! Iterative procedure to xcompute Beta( 0.04;-0.08, 0.04) ! Non-Iterative procedure to xcompute dBetadX(-0.08; 0.04, 0.04) ! Iterative procedure to xcompute Beta( 0.00;-0.04, 0.04) ! Non-Iterative procedure to xcompute d2AlphadX2(-0.04; 0.04) ! Iterative procedure to xcompute Gamma( 0.00;-0.08, 0.04,0.04) ! Iterative procedure to xcompute dAlphadX( 0.08;-0.08) ! Non-Iterative procedure to xcompute d2BetadX2(-0.08; 0.04, 0.04) ! ! ================================================================== ! A. Table 3 in paper number 1, ! O.Quinet, B.Champagne JCP 115,2481(2002) ! can be compared to the results from this run, of: ! ! Alpha tensor [in au]( -0.040000; 0.040000) ! x y z ! x. 11.502812 -0.000000 0.000000 ! y. -0.000000 11.502812 -0.000000 ! z. 0.000000 -0.000000 11.502811 ! ! Mean : 11.502812 ! Anisotropy : 0.000000 ! ! as well as ! ! mode 6(3186.7 cm^-1)( -0.040000; 0.040000) ! x y z ! x. 0.137838 -0.000000 -0.000000 ! y. -0.000000 0.137838 0.000000 ! z. -0.000000 0.000000 0.137838 ! ! Mean : 0.137838 ! Anisotropy : 0.000000 ! ! Raman ! Ak= 1.647939 Gk= 0.000002 ! Intensity= 122.2066 ! l-depolarization ratio=0.0000 ! n-depolarization ratio=0.0000 ! ! The mean 11.50 is to be compared to 16.09, and the mean 0.138 to ! the 0.191 in this table. The difference is due to the basis set. ! ! Table 6 also in paper 1 can be compared to: ! Raman Intensity at Omega = 0.040000 ! Intensity expressed in [Ang.^4/AMU] ! ---------------------------------------------------------------- ! Freq |Mult| Intensity (%) |l-depol ratio|n-depol ratio ! [cm^-1]| | | | ! ---------------------------------------------------------------- ! 1520.3| 3.| 9.29 ( 5.2)| 0.750000| 0.857143 ! 1739.8| 2.| 78.39 ( 44.2)| 0.750000| 0.857143 ! 3186.7| 1.| 122.21 ( 68.8)| 0.000000| 0.000000 ! 3280.0| 3.| 177.56 (100.0)| 0.750000| 0.857143 ! ---------------------------------------------------------------- ! ! aug-cc-pVDZ gives ! frequency= 1423.6 1637.6 3152.7 3266.1 ! Intensity= 0.03 7.78 226.85 160.44 ! which are much closer to the published POL result. To run this, ! use GBASIS=ACCD, MWORDS=10, ISPHER=1, and x=y=z=0.6289602528 ! ! ================================================================== ! B. Table 3 in paper number 2, ! O.Quinet, B.Champagne, B.Kirtman JCC 22, 1920(2001) ! can be compared to the results from this run, for d2Alpha/dX2: ! ! dQ( 6)(w=3186.7 cm^-1)dQ( 6)(w=3186.7 cm^-1)( -0.040000; 0.040000) ! x y z ! x. 0.001616 0.000000 -0.000000 ! y. 0.000000 0.001616 0.000000 ! z. -0.000000 -0.000000 0.001616 ! ! Mean : 0.001616 ! Anisotropy : 0.000000 ! ! The mean of 0.001616 is to be compared to the table's 0.002132. ! The 16.09 for dAlpha/dX was already reported in the 1st paper. ! ! Table 6 in paper 2 cannot be directly compared. The zero ! point value averaged results require a portion of the third ! nuclear derivative, E-abb, in addition to the polarizability ! derivative tensors computed analytically here. The paper ! obtained third nuclear deriviatives numerically, from E-ab, ! with a special code that is not included here. ! ! ================================================================== ! C. Table 3 in paper number 3, (this paper uses 0.042823, not 0.04) ! O.Quinet, B.Champagne JCP 117,2481(2002) ! can be compared to the results from this run, of: ! ! mode 6(3186.7 cm^-1)( -.080000; .040000, .040000) ! x y z ! xx. .000000 .000000 .000000 ! xy. .000000 .000000 -.593060 ! xz. .000000 -.593060 .000000 ! yx. .000000 .000000 -.593060 ! yy. .000000 .000000 .000000 ! yz. -.593060 .000000 .000000 ! zx. .000000 -.593060 .000000 ! zy. -.593060 .000000 .000000 ! zz. .000000 .000000 .000000 ! ! x : .000000 B(i)=(B(i,j,j)+B(j,i,j)+B(j,j,i))/5 ! y : .000000 ! z : .000000 ! BAR : .000000 BAR=B(i)*MU(i)/|MU| ! ! x : .000000 B(i)=(B(i,j,j)+B(j,i,j)+B(j,j,i))/3 ! y : .000000 ! z : .000000 ! VEC : .000000 norm of Beta VEC ! ! hyper-Raman ! Biii^2= .120590 Bijj^2= .080393 Bijk^2= .000000 ! Intensity= 976.5023 ! l-depolarization ratio= .8000 ! n-depolarization ratio= .6667 ! ! The -0.5930 is to be compared to the Table's -0.3532. The A,B,C ! values are obtained by least squares fitting to several runs, ! stepping w from 0.00, 0.02, 0.04, ... 0.10 (see eq. 18 and 19) ! ! Table 6 in the same paper can be compared to: ! Hyper Raman Intensity at Omega = 0.040000 ! Intensity expressed in [Ang.^6 AMU^-1 StatVolt^-2] ! ---------------------------------------------------------------- ! Freq |Mult| Intensity (%) |n-depol ratio|p-depol ratio ! [cm^-1]| | | | ! ---------------------------------------------------------------- ! 1520.3| 3.| 616.32 ( 63.1)| 0.266253| 0.153571 ! 1739.8| 2.| 0.01 ( 0.0)| 2.000000|************* ! 3186.7| 1.| 976.50 (100.0)| 0.800000| 0.666667 ! 3280.0| 3.| 845.50 ( 86.6)| 0.490350| 0.324810 ! ---------------------------------------------------------------- ! ! The 976.50 is to be compared to 346.4 in the published table, ! with the large discrepancy due to the small basis set used here. ! The aug-cc-pVDZ results are much closer to the table, ! frequency= 1423.6 1637.6 3152.7 3266.1 ! Intensity= 127.94 0.00 413.96 2063.99 ! ! ================================================================== ! D. Table 3 in paper number 4, ! O.Quinet, B.Kirtman, B.Champagne JCP 118,505(2003) ! can be compared to the results from this run, of: ! ! dQ( 6)(w=3186.7 cm^-1)dQ( 6)(w=3186.7 cm^-1) ! ( -.080000; .040000, .040000) ! x y z ! xx. .000000 .000000 .000000 ! xy. .000000 .000000 -.009749 ! xz. .000000 -.009749 .000000 ! yx. .000000 .000000 -.009749 ! yy. .000000 .000000 .000000 ! yz. -.009749 .000000 .000000 ! zx. .000000 -.009749 .000000 ! zy. -.009749 .000000 .000000 ! zz. .000000 .000000 .000000 ! ! x : .000000 B(i)=(B(i,j,j)+B(j,i,j)+B(j,j,i))/5 ! y : .000000 ! z : .000000 ! BAR : .000000 BAR=B(i)*MU(i)/|MU| ! ! x : .000000 B(i)=(B(i,j,j)+B(j,i,j)+B(j,j,i))/3 ! y : .000000 ! z : .000000 ! VEC : .000000 norm of Beta VEC ! ! in which the -0.0097 compares to -0.3532. ! Again the dispersion coefficients require fitting to multiple ! runs which step through w, and the ZPVA results require part ! of the third nuclear derivatives, not just the above tensor. ! $contrl scftyp=rhf runtyp=tdhfx nosym=1 ispher=0 $end $system timlim=3 $end $basis gbasis=n21 ngauss=3 $end $guess guess=huckel $end $scf dirscf=.true. conv=1d-6 $end $force method=analytic $end $cphf cphf=AO polar=.false. $end $tdhfx FREQ2 DADX 0.04 DADX_NI 0.04 DBDX 0.04 0.04 DBDX_NI 0.04 0.04 RAMAN 0.04 HRAMAN 0.04 D2ADX2_NI 0.04 D2BDX2_NI 0.04 0.04 $end $data methane RHF Td C 6.0 0.0 0.0 0.0 H 1.0 0.6252197764 0.6252197764 0.6252197764 $END