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Partitioning scheme for density functional calculations of extended systems
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10.1063/1.3106661
/content/aip/journal/jcp/130/14/10.1063/1.3106661
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/14/10.1063/1.3106661

Figures

Image of FIG. 1.
FIG. 1.

Schematics of two molecules and , and their partitioning into six regions: contact , buffer ( and ), and remote ( and ).

Image of FIG. 2.
FIG. 2.

Auxiliary systems enabling calculation of the total energy of the entire system: (a) subsystems and ; (b) subsystem (the “contact region”), and (c) subsystems and . Small solid circles correspond to possible LAs.

Image of FIG. 3.
FIG. 3.

Serine-water system: (a) geometry and atomic Mulliken charges after the full system geometry relaxation; all atoms in the pair are marked, and the charges (in electrons) are given in parenthesis; (b) subsystem containing water and a part of the serine molecule terminated with the LA; (c) subsystem containing only the part of the serine molecule of subsystem , also terminated with the same LA. (d) Comparison of system geometries relaxed using our partitioning method (bright) and when considering the hole system as one (dim). Oxygen atoms are red, H atoms white, C atoms green, and N atoms blue, while the LA is yellow.

Image of FIG. 4.
FIG. 4.

Lysine-water: (a) geometry and Mulliken charges (in brackets) on atoms obtained in the DFT calculation in which the whole system was considered as one; (b) the 13 atoms subsystem containing the LA at the position of carbon atom of the lysine molecule; (c) the corresponding subsystem; (d) a bigger 19 atoms subsystem , also terminated with the LA replacing atom ; and (e) the corresponding subsystem . (f) Two relaxed geometries of the lysine-water system, superimposed on each other: one obtained using our method with the smallest subsystem (bright) and the other when treating the pair as a single system (dim). The coloring system used is the same as in Fig. 3.

Image of FIG. 5.
FIG. 5.

Relative total energies of the lysine-water system as functions of the distance (in Å) between the two molecules (see insets where only the relevant part of the lysine molecule is shown) for three (chosen arbitrarily, see text) orientations of the water molecule, calculated using the exact method (solid lines) and our partitioning scheme (dashed lines). Note that geometry relaxation was not performed in these calculations. The total energies include the Coulomb correction at each point. These were however found to be very small (less than 0.02 eV). The zero energy corresponds to the exact energy minimum obtained with the exact method.

Image of FIG. 6.
FIG. 6.

Lysine dimer: (a) geometry of the dimer and Mulliken charges (in brackets) on atoms obtained in the DFT calculation in which the whole system was considered as one; (b) the smallest 20 atoms subsystem containing LAs on both sides at the positions of carbon atom of both molecules; (c) the corresponding subsystem (the subsystem, not shown, is built similarly from the other molecule); (d) a bigger 32 atoms subsystem , also terminated with two LAs at the position of and (e) the corresponding subsystem . (f) Two relaxed geometries of the lysine dimer, one obtained using our method with the smallest subsystem (partition 1) and the other when treating the dimer as a single system, superimposed on each other. The coloring system used is the same as in Fig. 3. Because of the symmetry, numbering of atoms and atomic charges are mainly shown only for one molecule for simplicity.

Image of FIG. 7.
FIG. 7.

A schematic comparison of the MFCC partitioning scheme (a) with ours (b) for the case of a single molecule divided into two fragments and . In the MFCC method, three artificial systems are considered: , , and the conjugated caps system . In our method five smaller subsystems are employed: (which is the fragment with a simple termination), ( with a termination), and , , and , the latter being essentially a superposition of and . Different semiovals designate the corresponding simple terminations (e.g., hydrogens) in both methods.

Tables

Generic image for table
Table I.

Comparison of angles (in degrees) and interatomic distances (in Å) in the lysine-water system calculated by (i) applying the DFT method to the whole system (second column) and (ii) using our method with both partitioning schemes. The results of our method are shown as deviations from the reference values in the second column and are presented in the third and fourth columns.

Generic image for table
Table II.

Comparison of Mulliken charges on atoms of the lysine-water system obtained using our partition method with subsystem containing 13 atoms (partitioning method 1), shown for different subsystems in columns 3–5, and after the reference calculation (the last column) in which the whole system was considered as one. The first column shows atom number according to Fig. 4(a), regions within molecule are shown in the second column. The charges without brackets obtained for subsystems and are used in our method as final atomic charges; the charges in the brackets do not represent the charges on atoms; however, they are needed to calculate the Coulomb correction, see Eq. (25).

Generic image for table
Table III.

Comparison of angles (in degrees) and interatomic distances (in Å) in the lysine dimer calculated by (i) applying the DFT method to the whole system (second column), (ii) using our partitioning method 1 (third column) and (iii) method 2 (fourth column). The results of our method are shown as deviations from the reference values in the second column and are presented in the third and fourth columns. Both the results calculated with the PBE and B3LYP (in brackets) functionals are shown.

Generic image for table
Table IV.

Comparison of Mulliken charges on atoms of the lysine dimer obtained using our partition method with subsystem containing 20 atoms (partitioning method 1), shown for different subsystems in columns 3–5, and after the exact calculation (the last column) in which the dimer was considered as one system. The PBE density functional was used. The first column shows atom number according to Fig. 6(a), regions within molecule are shown in the second column. Charges on atoms of the second molecule, subsystem , are not shown since these are the same on corresponding atoms due to symmetry. The charges without brackets obtained for subsystems and are used in our method as final charges on the atoms of the dimer; the charges in the brackets do not represent the charges on the dimer atoms; however, they are needed to calculate the Coulomb correction, Eq. (17).

Generic image for table
Table V.

Comparison of Mulliken charges on atoms of the lysine dimer obtained using our partition method with subsystem containing 32 atoms (partitioning method 2) and after the exact calculation. See the caption to Table IV for further details.

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/content/aip/journal/jcp/130/14/10.1063/1.3106661
2009-04-09
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Partitioning scheme for density functional calculations of extended systems
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/14/10.1063/1.3106661
10.1063/1.3106661
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