Hyperpolarizability of HF

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I first used B3LYP 6-311G++(2d,2p) by GAMESS to optimize HF, and then used NWCHEM7.0.0, GAMESS and Dalton2016.2 to calculate the hyperpolarizability of HF.

The NWCHEM input is

echo

start
memory stack 5500 mb heap 1500 mb global 7000 mb
geometry units angstroms print xyz
  symmetry c2v
H 0 0 -0.04648
F 0 0 0.87623
end

basis spherical
* library d-aug-cc-pVDZ
end

scf
 singlet
rhf
thresh 1.0e-8
end

tce
 scf
ccsd
maxiter 1000
thresh 1.0e-9
io ga
2eorb
2emet 13
tilesize 28
attilesize 40
end

set tce:lineresp T
set tce:leftresp T
set tce:respaxis T T T
set tce:afreq 0.0 0.0656
set tce:bfreq 0.0 0.0656

task tce energy
NWCHEM gives
CCSD Lambda Response polarizability / au
Frequency  =       0.0000000 / au
Wavelength = Infinity / nm
beta(Z,Z,Z) = 9.739286463 / au
...
CCSD Lambda Response polarizability / au
Frequency  =      -0.0656000 / au
Wavelength = -694.5633079 / nm
...
CCSD Quadratic Response
Static Hyperpolarizability       Why still called static?
-----------------------------------------------
beta(Z,Z,Z) = 8.461760589 / au
The original NWCHEM QA test using the following geometry

symmetry c2v
 H 0       0        0
F 0 0 1.7328795 in terms of a.u.

gives

CCSD Quadratic Response
Static Hyperpolarizability
-----------------------------------------------
...
beta(Z,Z,Z) = 8.630759039 / au

   1 H                    1.0000     0.00000000     0.00000000    -1.55959155
2 F 9.0000 0.00000000 0.00000000 0.17328795


Dalton2016.2 using the same basis set and c2v symmetry gives
 ZDIPLEN  (unrel.) -0.0000   ZDIPLEN  (unrel.)  0.0000   ZDIPLEN  (unrel.)  0.0000      8.8915460    
-0.1312 0.0656 0.0656 9.7304868

GAMESS HF gives using basis set accdz and c2v symmetry
 Beta tensor [in au]( -0.131200;  0.065600,  0.065600)
x y z
...
zz. -0.000000 -0.000000 -10.171063

Reference Frequency-dependent hyperpolarizability of hydrogen fluoride gives
static beta(z,z,z)=-8.058
SHG beta(z,z,z)=-9.430 at Re=1.7328 a.u.

Very Best Regards!
Edited On 7:57:14 AM PDT - Thu, Apr 2nd 2020 by Xiongyan21

Forum Vet
Threads 65
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I use the specific GAMESS input making software waMacMolPlt to redraw the molecule, then use mp2 and 6-311G++(2d,2p) to find the following equilibrium geometry of HF having c2v geometry

F            9.0   0.0000000000   0.0000000000   0.1048050057
H 1.0 0.0000000000 0.0000000000 -0.8135350057

With GAMESS
...
Beta tensor [in au]( -0.000000; 0.000000, 0.000000)
              x                y                z
zx. 0.704144 -0.000000 -0.000000
zz. -0.000000 -0.000000 9.926728
Beta tensor [in au]( -0.131200; 0.065600, 0.065600)
              x                y                z
xz. 0.848328 -0.000000 -0.000000
zx. 0.679234 -0.000000 -0.000000
zz. -0.000000 -0.000000 10.603235

The above reference gives (calculated)
SHG beta(zzz)=-9.430 beta(zxx)=-1.107 beta(xzx)=-1.276
static beta(zzz)=-8.722,-8.750 beta(zxx)=-1.045,-1.102
one indexed data there:static beta(zzz)=-9.838, beta(zxx)=-0.802
SCF:beta(zzz)=-8.808, beta(zxx)=-0.434

DALTO2016.2 gives
                 +---------------------------------------------------------------------------------------+
! FINAL CCSD RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
+---------------------------------------------------------------------------------------+


A operator B operator C operator property



ZDIPLEN (unrel.) -0.0000 ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 -8.6941344
-0.1312 0.0656 0.0656 -9.5090740









NWCHEM7.0.0 gives
CCSD Quadratic Response
Static Hyperpolarizability
-----------------------------------------------
beta(Z,X,X) = -0.770738651 / au
beta(Z,Z,Z) = -9.518810663 / au

CCSD Lambda Response polarizability / au
Frequency  =      -0.0656000 / au
Wavelength = -694.5633079 / nm

CCSD Quadratic Response
Static Hyperpolarizability
-----------------------------------------------

beta(X,Z,X) = -0.581141625 / au
beta(Z,X,X) = -0.581141625 / au
beta(Z,Z,Z) = -8.275124709 / au

Reference Ab initio variational calculation of dynamic polarizabilities and hyperpolarizabilities I. Polarizability and quadratic hyperpolarizability of water, carbon monoxide and hydrogen fluoride gives the transformed experimental beta parallel of -5.45 at 694 nm, i.e., from reference Measurements of second- and third-order nonlinear polarizabilities for HF and HCI .

Dalton2016.2 HF gives, using d-aug-cc-pv-dz,

B-freq = 0.065600 C-freq = 0.065600 beta(Z;Z,Z) = -8.06145767
B-freq = 0.065600 C-freq = 0.065600 beta(Z;X,X) = 0.11285876
B-freq = 0.065600 C-freq = 0.065600 beta(X;Z,X) = -0.00022904
beta parellel=-1/5(3*8.06146-2*0.112859+4*0.00022904)=-4.79

GAMESS gives
beta parellel=-1/5(3*10.603235+2*0.679234+4*0.848328)=-7.31

NWCHEM7.0.0 gives
beta parallel-1/5(3*8.275+2*0.5811+4*0.5811)=-5.66

Beta parallel is calculatd baseed on Prof. Jorgensen's article Frequency dependent hyperpolarizability of hydrogen fluoride.
I am trying to repeat this for HF and calculate this organic molecules in solutions.


Very Best Regards!
Edited On 3:26:53 AM PDT - Tue, Apr 7th 2020 by Xiongyan21

Forum Vet
Threads 65
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CCSDT level calculation of this failed
...
CCSDT Linear Response polarizability / au 
Frequency = 0.0656000 / au

                    

Frequency =       0.0000000 / au

CCSDT-YR (Static) iterations
---------------------------------------------
Iter Residuum Cpu Wall
---------------------------------------------
key = 90
1 0
2 10
3 19
tce_hash: key not found 0
------------------------------------------------------------------------
------------------------------------------------------------------------
current input line :
0:
------------------------------------------------------------------------
------------------------------------------------------------------------
This error has not yet been assigned to a category
------------------------------------------------------------------------
For more information see the NWChem manual at https://github.com/nwchemgit/nwchem/wiki


For further details see manual section: No section for this category                                                                                                                                                                                                                                   


MPI_ABORT was invoked on rank 2 in communicator MPI COMMUNICATOR 3 DUP FROM 0
with errorcode -1.

NOTE: invoking MPI_ABORT causes Open MPI to kill all MPI processes.
You may or may not see output from other processes, depending on
exactly when Open MPI kills them.



The ccsd(t) level calculation only gives ccsd hyperpolarizability and ccsd(t) energy, etc.


I have put the log files on Github.
Edited On 1:34:40 AM PDT - Sun, Mar 22nd 2020 by Xiongyan21

Forum Vet
Threads 65
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I have run the recently implemented ducc and the hyperpolarizability calculation sequentially using 5 threads, and it works. I have put the log file on Github.

Very Best Regards!

Forum Vet
Threads 65
Posts 307
I have run the recently implemented ducc and the hyperpolarizability calculation sequentially using 5 threads,all at ccsd level, and it works. I have put the log file on Github.

Very Best Regards!

Forum Vet
Threads 65
Posts 307
Measurements and Calculations of the Hyperpolarkabilities of Atoms and Small Molecules in the Gas Phase gives experimental beta=-11.0+-1.0 a.u. at 694.3 nm.

Table XIII. in this Chemical Reviews article gives beta (parallel) of -7.3 a.u. using ab initio.
Edited On 1:43:11 AM PDT - Sun, Apr 5th 2020 by Xiongyan21

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Threads 65
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According to Table VIII in reference Molecular vibrational and rotational motion in static and dynamic fields, axial beta(vibrational) calculated can be 10.041,10.99 and 10.51, and beta(averaged over the vibrational gound state) calculated can be -10.505 and -8.47. It is stated in this reference there is a radical change in beta(zzz) when vibration is taken into consideration. GAMESS can calculate hyper-raman spectra. It is also said the discrepency betweem the calculated and the theoretical one is caused by the measured is for HF dimer.

I use 6-311G++(2d,2p) and mp2 with GAMESS to optimize initially linear HF dimer, get an nonlinear, planar equilibrium geometry, and then find the hyper-Raman spectra have five additional peaks when compared with those of the monomer, but its beta(zzz)es become zero or nearly zero, with the following similar in the position of this peak

monomer:
Hyper-Raman Intensity at omega = 0.065600
    Intensity expressed in [Ang.^6 AMU^-1 StatVolt^-2]
----------------------------------------------------------------
Freq |Mult| Intensity (%) |n-depol ratio|p-depol ratio
[cm^-1]| | | |
----------------------------------------------------------------
4102.4| 1.| 607.41 (100.0)| 0.259696| 0.149225
----------------------------------------------------------------

...

dimer
Hyper-Raman Intensity at omega = 0.065600
    Intensity expressed in [Ang.^6 AMU^-1 StatVolt^-2]
----------------------------------------------------------------
Freq |Mult| Intensity (%) |n-depol ratio|p-depol ratio
[cm^-1]| | | |
----------------------------------------------------------------
...
4122.9| 1.| 420.37 (100.0)| 0.304597| 0.179661
----------------------------------------------------------------

The optimization of an initially nonlinear dimer gets an nonlinear, planar geometry and gives
Hyper Raman Intensity at omega = 0.065600
    Intensity expressed in [Ang.^6 AMU^-1 StatVolt^-2]
----------------------------------------------------------------
Freq |Mult| Intensity (%) |n-depol ratio|p-depol ratio
[cm^-1]| | | |
----------------------------------------------------------------
4122.6| 1.| 420.66 (100.0)| 0.304631| 0.179684
----------------------------------------------------------------
and five additional peaks as well as around zero beta(zzz)es.


From the dimer optimized structure, 276.76 pm is the distance between the two Fs, 92 pm is the length of each of the F-H bond, and 185.71 pm is the intermolecular hydrogen bond length. These agree with those in reference Benchmark calculations with correlated molecular wave functions. VII. Binding energy and structure of the HF dimer, where the dimer has no intermolecular hydrogen bond.

Very Best Regards!
Edited On 2:00:26 AM PDT - Mon, Apr 6th 2020 by Xiongyan21

Forum Vet
Threads 65
Posts 307
To my dismay, the aug-cc-pvdz CCSD calculation of beta(ZZZ) of HF using DALTON2016.2 and NWCHEM7.0.0 can give around -13.501 a.u., and around -11.795 a.u., respectively. NWCHEM 7.0.0 can give chi(parallel) around -4.53*10^-32 esu, close to the experimental value -4.70*10^-32 esu., but with d-aug-cc-pvdz, CCSD in NWCHEM7.0.0 only gives that of around-2.88*10^-32 esu.


No obvious changes caused by the employment of aug-cc-pvdz instead of d-aug-cc-pvdz using Dalton2016.2 and accd instead of accdc using GAMESS.

The optimization of an HF dimer with 6-311G++(2d,2p) and mp2 using GAMESS can give five additional hyper-Raman peaks and all around zero beta(zzz)es.

With HF Dalton2016.2 gives chi(parallel) around -3.58*10^-32 esu. , and GAMESS gives that around -3.68*10^-32 esu.

I will try the hyper-Raman of all-trans retinal and compare it with the experimental one.

Very Best Regards!
Edited On 7:01:50 PM PDT - Mon, Apr 6th 2020 by Xiongyan21


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