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### Automatically generated Coulomb fitting basis sets: Design and accuracy for systems containing H to Kr

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1 Department of Computer Science, ANU College of Engineering and Computer Science, The Australian National University, Canberra ACT 0200, Australia
2 Gaussian Inc., Wallingford, Connecticut 06492
J. Chem. Phys. 127, 074102 (2007)
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### References

• Rui Yang , Alistair P. Rendell  and Michael J. Frisch
• Source: J. Chem. Phys. 127, 074102 ( 2007 );
1.
1.L. Greengard and V. Rokhlin, J. Comput. Phys. 73, 325 (1987).
http://dx.doi.org/10.1016/0021-9991(87)90140-9
2.
2.C. A. White and M. Head-Gordon, J. Chem. Phys. 101, 6593 (1994).
http://dx.doi.org/10.1063/1.468354
3.
3.K. Eichkorn, F. Weigend, O. Treutler, and R. Ahlrichs, Theor. Chem. Acc. 97, 119 (1997).
http://dx.doi.org/10.1007/s002140050244
4.
4.K. Eichkorn, O. Treutler, H. Ohm, M. Häser, and R. Ahlrichs, Chem. Phys. Lett. 240, 283 (1995).
http://dx.doi.org/10.1016/0009-2614(95)00621-A
5.
5.F. Weigend, Phys. Chem. Chem. Phys. 4, 4285 (2002).
http://dx.doi.org/10.1039/b204199p
6.
6.F. Weigend, Phys. Chem. Chem. Phys. 8, 1057 (2006).
http://dx.doi.org/10.1039/b515623h
7.
7.F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997).
http://dx.doi.org/10.1007/s002140050269
8.
8.F. Weigend, M. Häser, H. Patzelt, and R. Ahlrichs, Chem. Phys. Lett. 194, 143 (1998).
9.
9.F. Weigend, A. Köhn, and C. Hättig, J. Chem. Phys. 116, 3175 (2002).
http://dx.doi.org/10.1063/1.1445115
10.
10.M. W. Feyereisen, G. Fitzgerald, and A. Kormonicki, Chem. Phys. Lett. 208, 359 (1993).
http://dx.doi.org/10.1016/0009-2614(93)87156-W
11.
11.D. E. Bernholdt and R. J. Harrison, Chem. Phys. Lett. 250, 477 (1996).
http://dx.doi.org/10.1016/0009-2614(96)00054-1
12.
12.D. E. Bernholdt and R. J. Harrison, J. Chem. Phys. 109, 1593A (1998).
13.
13.A. A. Bibikov, V. Zayets, and I. Bodrenko, J. Chem. Phys. 123, 024103 (2005).
http://dx.doi.org/10.1063/1.1947193
14.
14.T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).
http://dx.doi.org/10.1063/1.456153
15.
15.D. E. Woon and T. H. Dunning, J. Chem. Phys. 98, 1358 (1993).
http://dx.doi.org/10.1063/1.464303
16.
16.J. Andzelm and E. Winner, J. Chem. Phys. 96, 1280 (1991).
http://dx.doi.org/10.1063/1.462165
17.
17.W. J. Hehre, L. Radom, and P. v. R. Schleyer, Ab Initio Molecular Orbital Theory (Wiley, New York, 1986).
18.
18.P. C. Hariharan and J. A. Pople, Chem. Phys. Lett. 217, 66 (1972).
19.
19.N. Godbout, D. R. Salahub, J. Andzelm, and E. Wimmer, Can. J. Chem. 70, 560 (1992).
http://dx.doi.org/10.1139/v92-079
20.
20.C. Sosa, J. Andzelm, B. C. Elkin, E. Wimmer, K. D. Dobbs, and D. A. Dixon, J. Phys. Chem. 96, 6630 (1992).
http://dx.doi.org/10.1021/j100195a022
21.
21.M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN03, Revision C.02 (Gaussian, Inc., Wallingford, CT, 1983).
22.
22.L. laaksonen, P. Pyykkö, and D. Sundholm, Int. J. Quantum Chem. 23, 319 (1983).
http://dx.doi.org/10.1002/qua.560230127
23.
23.D. Sundholm, P. Pyykkö, and L. Laaksonen, Mol. Phys. 56, 141 (1985).
24.
24.P. Pyykkö, D. Sundholm, and L. Laaksonen, Mol. Phys. 60, 595 (1987).
25.
25.In the released version of GAUSSIAN03 and for the results reported here the value of the largest exponent was not doubled. Subsequent tests show that whether this exponent is doubled or not has no significant effect on the results presented in this paper or the conclusions.
26.
26.A. Schäfer, H. Horn, and R. Ahlrichs, J. Chem. Phys. 97, 2571 (1992).
http://dx.doi.org/10.1063/1.463096
27.
27.A. Schäfer, C. Huber, and R. Ahlrichs, J. Chem. Phys. 100, 5829 (1994).
http://dx.doi.org/10.1063/1.467146
28.
28.N. B. Balabanov and K. A. Peterson, J. Chem. Phys. 123, 064107 (2005).
http://dx.doi.org/10.1063/1.1998907
29.
29.A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper, and J. Olsen, Chem. Phys. Lett. 302, 437 (1999).
http://dx.doi.org/10.1016/S0009-2614(99)00179-7
30.
30.A. D. Becke, Phys. Rev. A 38, 3098 (1988).
http://dx.doi.org/10.1103/PhysRevA.38.3098
31.
31.A. D. Becke, Phys. Rev. A 98, 5648 (1993).
32.
32.J. P. Perdew, Phys. Rev. B 33, 8822 (1986).
http://dx.doi.org/10.1103/PhysRevB.33.8822
33.
33.Improved auxiliary basis sets, Cartesian coordinates of the test set molecules, and statistical evaluation data, Electronic Supplementary Information for PCCP Paper b515623h, i.e., Ref. 6. The first-row molecular test set contains the following 56 compounds with the heaviest element to be first-row elements: , , , , , , , , , , , , LiCl, LiF, LiH, , , , , , , , , , , , , , , , , , , , CO, , , , , , , HCN, HF, HNC, HNO, , , , , , , , , , and . The second-row molecular test set contains the following 46 compounds with the heaviest element to be second-row elements: BeS, , LiCl, LiSLi, , , MgF, , , , , , , NaCl, NaF, NaH, , , , , , , AlN, , ClF, , , , HCP, HCl, HSH, HSSH, , , , , , , , , , , , , , and . The third-row molecular test set contains the following 78 compounds with the heaviest element to be third-row elements: , , KCl, KF, KH, , , , KBr, , , AsCl3, , , , GaCl, , GaF, , , GaO, , , , , GeO, , , , SeO, , , , , , , , , , , , CuCN, CuCl, CuF, CuH, , , , FeO, , , MnO, , , , MnS, , , , , NiO, NiS, , , , , , TiO, , , , VO, , , , , BrCl, and .
34.
34.F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys. 7, 3297 (2005).
http://dx.doi.org/10.1039/b508541a
35.
35.W. Armstrong, P. Christen, E. McCreath, and A. P. Rendell, Proceedings of the International Workshop on Integration AI and Data Mining, 2006, Los Alamitos, CA, 2006, pp. 1824, .
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/7/10.1063/1.2752807

## Figures

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FIG. 1.

The dependence of the HF Coulomb energy fitting error and the atomization energy fitting error on the size of OBS for the auto-ABS, DGA1, DGA2, and cc-pVXZ (, 5, and 6) fitting sets for polyatomic molecules (a) and (b) .

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FIG. 2.

The dependence of the HF Coulomb energy fitting error on the size of ABS for the auto-ABS, DGA1, DGA2, and cc-pVXZ (, 5, and 6) fitting sets for polyatomic molecules (a) and (b) .

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FIG. 3.

Diagram showing the relationship between the number of functions in the OBS for a nitrogen atom and the number of functions in the ABS when generated using , 1.7, and 2.0. Trend lines have been calculated using linear least-squares fit.

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FIG. 4.

Variation of the size scaling factor for fitting basis sets generated via auto-ABS as a function of and for all atoms from H to Ne.

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FIG. 5.

The dependence of the error in the Coulomb energy on the size of OBS for the auto-ABS generated with , 1.7, and 2.0 for polyatomic molecules (a) and (b) . Also shown is the error in the HF energy .

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FIG. 6.

The dependence of the error in the Coulomb energy on the size of ABS for the auto-ABS generated with , 1.7, and 2.0 for polyatomic molecules (a) and (b) .

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FIG. 7.

Relative performance for a BLYP DFT calculation using four different methods for computing the Coulomb contribution, normal, fast multiple method (FMM), and density fitting with either a DGA2 or auto-ABS fitting basis. Ratios are relative to the normal total times. Results obtained using a cc-pVTZ and 3-21g basis for (a) 18-Crown-6 ether and (b) valinomycin, respectively. Data obtain using GAUSSIAN03 on a Itanium processor.

## Tables

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Table I.

Number of functions in the OBS and ABS , errors in the HF energy due to basis set incompleteness (, in ), and the error in the Coulomb energy (, in ) using auto-ABS with for atoms H, He, Li, N, Ne, Na, P, Ar, Cu, As, and Kr and for a variety of popular OBSs.

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Table II.

Number of functions in the OBS and ABS , errors in the HF energy due to basis set incompleteness (, in ), and errors in the Coulomb energy (, in ) using auto-ABS with for diatomic molecules , BH, HF, , CO, BF, and and polyatomic molecules and and for a variety of popular OBSs.

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Table III.

The fitting error per atom (in ) in the Coulomb energy and atomization energy computed using auto-ABS for cc-pVXZ (, T, Q, and 5) OBSs and the following compounds: , NaCl, , , , , , , , , , and .

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Table IV.

The maximum errors in bond lengths ( in pm), angles ( in deg), dipole moments ( in D), and selected quadrupole moments ( in ) at optimized structures for selected molecules containing atoms H–Kr using the auto-ABS in conjunction with cc-pVXZ (, T, Q, and 5) OBSs.

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Table V.

Values for the mean and standard deviation for per atom and obtained using the universal ABS (Ref. 6) and auto-ABS with , 2.0, and 2.5 for selected molecule sets and using def2-SV(P), def2-TZVP and def2-QZVPP OBSs. See text for definition of the molecule sets.

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2013-12-05

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Scitation: Automatically generated Coulomb fitting basis sets: Design and accuracy for systems containing H to Kr
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/7/10.1063/1.2752807
10.1063/1.2752807
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