DFTB can undermine alpha, beta and gamma significantly

[xiongyan21]

DFTB can undermine alpha, beta and gamma significanlty , which may cause large discrepancies when compared with experimental data or results from other methods in GAMESS.

Very Best Regards!

[xiongyan21]

For the nearly plananr 3-methoxyaniline, alpha by DFTB3 with a DFTB3 optimized geometry is 65.33, and beta is around 206, significantly lower than those, both of which can be compared with those from mp2 finite field differencing (6-311G) of an mp2 optimized geometry(6-31+G)(RE within 7%), in Spectroscopic (FT-IR, FT-Raman and NMR) and computational studies on 3- methoxyaniline(HF) .

Dalton 2020 CCS level of beta gives a relative deviance of ~14.5%. compared with that in the reference, and a relative error within 7% , compared with GAMESS mp2 finite difference field result.

GAMESS TDHF almost can reproduce alpha in the reference, and gives static beta with the absolute deviance fronm the CCS data of around 11, according to the formula in the reference. When two zero frequencies are employed, GAMESS DFT can give beta(2,1,1) , beta(1,1,2) and beta(1,2,1) all around 211, and when one 0.0856 a.u. is used, the Kerr beta value is close to CCS calculated results.

NWCHEM7.02 gives alpha a deviance around 8% from the data in the reference.

Very Best Regards!

[xiongyan21]

The above are the the results based on energy from the finite field differencing mp2 method, and A keyword, will be added, although perhaps time-consuming, to discover whether there are numerical issues by obtainiing dipole based results.

ACCD basis set gives alpha around 100 with mp2 finite field , as well as beta , and NWCHEM7.0.2 DFT gives alpha around 88. 6-311++G(2d,2p) mp2 finite field differencing gives beta colose to the above. Gamma for 3-methoxyaniline is also obtained.

For pyrrole, accd and 6-311++G(2d,2p) mp2 finite field differencing all give alpha close to the experimental values indexed in Theoretical Investigation of the (Hyper)polarizabilities of Pyrrole Homologues C 4 H 4 XH (X ) N, P, As, Sb, Bi). A Coupled-Cluster and Density Functional Theory Study, and beta(vec) of the former close to mp2 value, and the latter close to CCSD(T) one, respectively in the reference, but gammas may be significantly different.

With Dalton2020, CC2 beta of pyrrole is |E%| iwithin 15% form the CCSD(T) result in the reference.

MP2 finite field differencing is perhaps significantly faster than CCSD, and CC3 methods.

Very Best Results.

[xiongyan21]

When the keyword is added into $mp2 in test pol-ffield-ims, one can get the following

             ----ENERGY BASED RESULTS----

DIPOLE # X Y Z (A.U.) ###################################################################

0.0000000E+00 1.6396877E+00 -1.5519872E+00

ALPHA # X Y Z (A.U.) ################################################################### X # 1.6378620E+12 -2.3768128E-04 -1.1932570E-03 Y # -2.3768128E-04 1.6378620E+12 2.1730860E-03 Z # -1.1932570E-03 2.1730860E-03 1.6378620E+12

BETA # X Y Z (A.U.) ################################################################### XX # 6.9849193E-01 -2.2118911E+00 -3.1432137E+00 YY # 0.0000000E+00 -1.4551915E+00 -1.1641532E+00 ZZ # 0.0000000E+00 -1.0477379E+00 -2.1536835E+00

GAMMA # XX YY ZZ (A.U.) ################################################################### XX # -3.9308688E+18 -2.6205792E+18 -2.6205792E+18 YY # -2.6205792E+18 -3.9308688E+18 -2.6205792E+18 ZZ # -2.6205792E+18 -2.6205792E+18 -3.9308688E+18

               ----DIPOLE BASED RESULTS----

DIPOLE # X Y Z (A.U.) ###################################################################

0.0000000E+00 1.6396874E+00 -1.5519881E+00

ALPHA # X Y Z (A.U.) ################################################################### X # 2.4340650E-03 0.0000000E+00 0.0000000E+00 Y # 0.0000000E+00 2.6261107E-03 1.7878989E-04 Z # 0.0000000E+00 1.7878861E-04 1.6674370E-03

BETA # X Y Z (A.U.) ################################################################### XX # 0.0000000E+00 0.0000000E+00 0.0000000E+00 YY # 0.0000000E+00 0.0000000E+00 0.0000000E+00 ZZ # 0.0000000E+00 0.0000000E+00 0.0000000E+00

GAMMA # XX YY ZZ (A.U.) ################################################################### XX # 0.0000000E+00 0.0000000E+00 0.0000000E+00 YY # 0.0000000E+00 1.4921397E-04 -4.5474735E-04 ZZ # 0.0000000E+00 -4.5474735E-04 0.0000000E+00

When accd basis set is employed, the two have no significant difference for alpha.

----ENERGY BASED RESULTS----

DIPOLE # X Y Z (A.U.) ###################################################################

0.0000000E+00 0.0000000E+00 0.0000000E+00

ALPHA # X Y Z (A.U.) ################################################################### X # 4.7855840E+00 0.0000000E+00 0.0000000E+00 Y # 0.0000000E+00 4.7855847E+00 0.0000000E+00 Z # 0.0000000E+00 0.0000000E+00 3.7380685E+00

BETA # X Y Z (A.U.) ################################################################### XX # 2.1316282E-04 -4.5474735E-04 -4.1353587E-03 YY # 0.0000000E+00 -3.6948222E-04 6.8922645E-03 ZZ # 3.8795633E-03 -7.7449158E-03 0.0000000E+00

GAMMA # XX YY ZZ (A.U.) ################################################################### XX # 1.3694716E+03 2.1651658E+02 2.0961930E+06 YY # 2.1651658E+02 1.3679369E+03 2.0961509E+06 ZZ # 2.0961930E+06 2.0961509E+06 1.6532908E+02

               ----DIPOLE BASED RESULTS----

DIPOLE # X Y Z (A.U.) ###################################################################

0.0000000E+00 0.0000000E+00 0.0000000E+00

ALPHA # X Y Z (A.U.) ################################################################### X # 4.7858964E+00 0.0000000E+00 0.0000000E+00 Y # 0.0000000E+00 4.7858964E+00 0.0000000E+00 Z # 0.0000000E+00 0.0000000E+00 3.7381877E+00

BETA # X Y Z (A.U.) ################################################################### XX # 0.0000000E+00 0.0000000E+00 0.0000000E+00 YY # 0.0000000E+00 0.0000000E+00 0.0000000E+00 ZZ # 0.0000000E+00 0.0000000E+00 0.0000000E+00

GAMMA # XX YY ZZ (A.U.) ################################################################### XX # 3.1185741E+02 1.0082904E+02 1.1082624E+02 YY # 1.0082904E+02 3.1183188E+02 1.1408293E+02 ZZ # 1.1082624E+02 1.1408293E+02 4.4570663E+00

It is still necessary to evaluate beta and gamma to discover whether any numerical differencing error could be eliminated.

The words in the original test are humorous " more digits are printed in the polarizabilities than can be
justified - no experiment can measure this, ", making the sophisticated computational quantum chemistry interesting.

Those for 3-methoxyaniline are also being evaluated.

Very Best Regards!

[xiongyan21]

Accd basis set mp2 finite field differecing of 3-methoxyaniline can get the same alpha and similar beta, but quite different gamma. 6-311++G(2d,2p) gives the following for the test

----ENERGY BASED RESULTS----

DIPOLE # X Y Z (A.U.) ###################################################################

0.0000000E+00 0.0000000E+00 0.0000000E+00

ALPHA # X Y Z (A.U.) ################################################################### X # 3.4856471E+00 0.0000000E+00 -3.1108631E-02 Y # 0.0000000E+00 3.4856473E+00 -3.1109494E-02 Z # -3.1108631E-02 -3.1109494E-02 2.7393338E+00

BETA # X Y Z (A.U.) ################################################################### XX # 4.2632564E-04 -1.2789769E-04 -2.7000624E-04 YY # 0.0000000E+00 -5.4711791E-04 1.8474111E-04 ZZ # 2.2737368E-04 -3.2684966E-04 0.0000000E+00

GAMMA # XX YY ZZ (A.U.) ################################################################### XX # 1.8986270E+03 1.1810926E+03 1.1342536E+03 YY # 1.1810926E+03 1.8999913E+03 1.1348220E+03 ZZ # 1.1342536E+03 1.1348220E+03 1.5312196E+03

               ----DIPOLE BASED RESULTS----

DIPOLE # X Y Z (A.U.) ###################################################################

0.0000000E+00 0.0000000E+00 0.0000000E+00

ALPHA # X Y Z (A.U.) ################################################################### X # 3.4864303E+00 0.0000000E+00 0.0000000E+00 Y # 0.0000000E+00 3.4864302E+00 0.0000000E+00 Z # 0.0000000E+00 0.0000000E+00 2.7400425E+00

BETA # X Y Z (A.U.) ################################################################### XX # 0.0000000E+00 0.0000000E+00 0.0000000E+00 YY # 0.0000000E+00 0.0000000E+00 0.0000000E+00 ZZ # 0.0000000E+00 0.0000000E+00 0.0000000E+00

GAMMA # XX YY ZZ (A.U.) ################################################################### XX # 2.4891946E+02 8.2862462E+01 7.2997993E+06 YY # 8.2862462E+01 2.4904383E+02 7.3043965E+06 ZZ # 7.2997993E+06 7.3043965E+06 -8.3675910E+01

Very Best Regartds!

[xiongyan21]

6-311++G(2d,2p) mp2 finite field differencing gives the dipole based beta and gamma of 3-methoxyanilinine a maximum absolute deviance of around 3.6% and 8.9%, compared with those based on energy. respectively, and that of around 2.6% and 7% compared with beta and gamma based on energy with accd, respectively.

Very Best Regards!