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! 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