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Accurate basis set truncation for wavefunction embedding
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10.1063/1.4811112
/content/aip/journal/jcp/139/2/10.1063/1.4811112
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/2/10.1063/1.4811112

Figures

Image of FIG. 1.
FIG. 1.

(a) The BK-1 water hexamer, with molecule numbering indicated. (b) Illustration of the atom sets defined in Sec. III B , with one possible choice of the active, border, and distant atoms indicated.

Image of FIG. 2.
FIG. 2.

(a) HF-in-HF embedding error for molecule 1 of the BK-1 water hexamer. The solid curve provides the supermolecular embedding results, while the results of naive truncation of the AO basis set are shown in the dashed curve. Also shown is the effect of partitioning the projection operator for HF-in-HF embedding in the truncated basis set, with either {μ′, μ″} = {μ, 0} (dashed-dotted) or {μ′, μ″} = {10, μ} (crosses). (b) The corresponding truncation error for the CCSD(T)-in-HF truncated embedding calculations.

Image of FIG. 3.
FIG. 3.

(a) The number of MOs assigned to as a function of τ for the BK-1 conformation of the water hexamer. The sets of active and border atoms correspond to the case shown in Fig. 1(b) . (b) The absolute error in the HF-in-HF embedding calculation as a function of τ. The data point on the far right is equivalent to the dashed-dotted curve in Fig. 2(a) at μ′ = 10, while the data point on the far left is equivalent to the cross at μ″ = 10. Thus changing τ corresponds to switching between the dashed-dotted curve and the set of crosses in Fig. 2(a) . (c) The absolute error in the HF-in-HF embedding calculation as a function of the border atom cutoff, .

Image of FIG. 4.
FIG. 4.

(a) The effect of varying on the HF-in-HF/cc-pVDZ embedding energy of the BK-1 conformation of the water hexamer. Each curve corresponds to assigning the constituent atoms of the indicated molecule as the set of active atoms. For a cutoff of 2.0 Å, the calculation is equivalent to a monomolecular calculation using TF embedding and no projection operator. At 6.0 Å, all of the calculations are performed in the supermolecular basis, and the projection operator is used exclusively with no approximate functionals. (b) The corresponding CCSD(T)-in-HF/cc-pVDZ results. (c) The corresponding HF-in-HF/aug-cc-pVDZ results. (d) The corresponding CCSD(T)-in-HF/aug-cc-pVDZ results.

Image of FIG. 5.
FIG. 5.

The Gly-Gly-Gly-Gly tetrapeptide, with the set of active atoms comprised of the Gly2 residue (solid red box). Each of the dashed boxes indicates the union of the sets of active and border atoms for the corresponding value of ; any atoms outside of the boxes are included in the set of distant atoms.

Image of FIG. 6.
FIG. 6.

(a) τ-dependence of the number of projected orbitals within MP2-in-HF/aug-cc-pVDZ truncated embedding calculations on the Gly-Gly-Gly-Gly tetrapeptide with = 3. The choice of active and border atoms is indicated in Fig. 5 . (b) μ′-dependence of the truncation error of this calculation for several values of τ.

Image of FIG. 7.
FIG. 7.

(a) Convergence of the truncation error of embedding calculations on the Gly-Gly-Gly-Gly tetrapeptide using the cc-pVDZ basis set and several values of . In each curve, the set of active atoms corresponds to the indicated residue. For = 9, there are no distant atoms in any of the calculations. (b) The corresponding calculation using the aug-cc-pVDZ basis set. The inset shows the same results on a larger scale.

Image of FIG. 8.
FIG. 8.

(a) Energies of water hexamer conformations obtained using both CCSD(T) over the full system and CCSD(T)-in-HF supermolecular EMBE2 calculations. Three different basis sets are employed, with the cc-pVDZ and aug-cc-pVDZ basis sets abbreviated as VDZ and AVDZ, respectively. Conformation energies are reported with respect to the corresponding calculation for Conf. 11. (b) Error in the energy of the EMBE2 calculations.

Image of FIG. 9.
FIG. 9.

Energies of water hexamer conformations obtained using both CCSD(T)-in-HF supermolecular EMBE2 calculations and CCSD(T)-in-HF truncated EMBE2 calculations. The embedding calculations employ truncated embedding with a border atom cutoff of either = 0 Å or = 3 Å. Conformation energies are reported with respect to the corresponding calculation for Conf. 11.

Image of FIG. 10.
FIG. 10.

Three of the Gly-Gly-Gly (GGG) tripeptide conformations are presented on the left for several different dihedral angles. The geometries of the Val-Pro-Leu (YPL) and Tyr-Pro-Tyr (YPY) tripeptides are presented on the right.

Image of FIG. 11.
FIG. 11.

(a) Gly-Gly-Gly tripeptide conformation energies obtained using MP2-in-HF EMBE2 calculations and employing the cc-pVDZ basis. Conformation energies are reported with respect to the corresponding calculation for the Ω = 180° conformation. The results using = 4 are not shown for this basis set, as they are nearly indistinguishable from the supermolecular results. (b) The corresponding results employing the aug-cc-pVDZ basis. The results using = 1 are not shown for this basis set, as they are highly inaccurate.

Tables

Generic image for table
Table I.

List of water molecules, the atoms of which comprise the set of border atoms for each value of in Fig. 3(c) . At = 3.0 Å, the set of border atoms is the same as that shown in Fig. 1(b) .

Generic image for table
Table II.

Summary of the EMBE2 results for the water hexamer test set. Results are listed using truncated embedding with a cutoff of = 0 Å, truncated embedding with a cutoff of = 3 Å, and supermolecular embedding. All values are in kcal/mol.

Generic image for table
Table III.

Summary of the EMBE2 results for the Gly-Gly-Gly tripeptide. All calculations use either the cc-pVDZ (VDZ) basis set or the aug-cc-pVDZ (AVDZ) basis set. Results are provided for several values of , as well as for the supermolecular basis set (Super.). Both the mean unsigned MBE error over all values of Ω and the standard deviation of the MBE error are provided. All values are reported in kcal/mol.

Generic image for table
Table IV.

The MBE error (Eq. (24) ) for the Val-Pro-Lue tripeptide, the Tyr-Pro-Tyr tripeptide, and the Gly-Gly-Gly-Gly tetrapeptide EMBE2 calculations. All calculations use either the cc-pVDZ (VDZ) basis set or the aug-cc-pVDZ (AVDZ) basis set. Results are provided for several values of , as well as for the supermolecular basis set (Super.). All values are reported in kcal/mol.

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/content/aip/journal/jcp/139/2/10.1063/1.4811112
2013-07-08
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Accurate basis set truncation for wavefunction embedding
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/2/10.1063/1.4811112
10.1063/1.4811112
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