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root/group/trunk/multipole/dielectric.aux
Revision: 4353
Committed: Tue Sep 15 15:56:07 2015 UTC (8 years, 9 months ago) by mlamichh
File size: 5752 byte(s)
Log Message:
Added new tex file for dielectric.

File Contents

# Content
1 \relax
2 \newlabel{FirstPage}{{}{1}{}{}{}}
3 \@writefile{toc}{\contentsline {title}{Real space electrostatics for multipoles. III. Dielectric Properties}{1}{}}
4 \@writefile{toc}{\contentsline {abstract}{Abstract}{1}{}}
5 \citation{Wolf99,Zahn02,Kast03,Beckd.A.C._Bi0486381,Ma05,Fennell06}
6 \citation{Wolf99}
7 \citation{Wolf99}
8 \citation{Allen:1989fp}
9 \citation{Neumann:1983mz,Neumann:1983yq,Neumann84,Neumann85}
10 \citation{Horn04}
11 \@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{2}{}}
12 \newlabel{eq:staticDielectric}{{1}{2}{}{}{}}
13 \newlabel{eq:KirkwoodFactor}{{2}{2}{}{}{}}
14 \newlabel{eq:fluctBoxDipole}{{3}{2}{}{}{}}
15 \@writefile{toc}{\contentsline {section}{\numberline {II}Dielectric constants for real-space electrostatics}{2}{}}
16 \citation{Neumann:1983mz,Neumann:1983yq}
17 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces With the real-space electrostatic methods, the effective dipole tensor, $\mathbf {T}$, governing interactions between molecular dipoles is not the same for charge-charge interactions as for point dipoles.}}{3}{}}
18 \newlabel{fig:stockmayer}{{1}{3}{}{}{}}
19 \citation{Neumann:1983yq}
20 \citation{Zahn02}
21 \citation{Izvekov:2008wo}
22 \citation{Allen:1989fp}
23 \citation{Adams:1980rt,Adams:1981fr,Neumann:1983yq}
24 \citation{Adams:1980rt,Adams:1981fr,Neumann:1983yq}
25 \@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Expressions for the dielectric correction factor ($A$) for the real-space electrostatic methods in terms of the damping parameter ($\alpha $) and the cutoff radius ($r_c$). The Ewald-Kornfeld result derived in Refs. \rev@citealpnum {Adams:1980rt,Adams:1981fr,Neumann:1983yq} is shown for comparison using the Ewald convergence parameter ($\kappa $) and the real-space cutoff value ($r_c$). }}{5}{}}
26 \newlabel{tab:A}{{I}{5}{}{}{}}
27 \@writefile{toc}{\contentsline {section}{\numberline {III}Boltzman average of the dipole polarization density}{5}{}}
28 \newlabel{eq:fluc}{{23}{6}{}{}{}}
29 \@writefile{toc}{\contentsline {section}{\numberline {IV}Boltzmann average of a quadrupole moment}{6}{}}
30 \newlabel{eq:1}{{25}{6}{}{}{}}
31 \newlabel{eq:2}{{26}{7}{}{}{}}
32 \newlabel{eq:3}{{27}{7}{}{}{}}
33 \newlabel{eq:4}{{28}{7}{}{}{}}
34 \newlabel{eq:5}{{29}{7}{}{}{}}
35 \newlabel{eq:6}{{30}{7}{}{}{}}
36 \newlabel{eq:7}{{31}{8}{}{}{}}
37 \@writefile{toc}{\contentsline {section}{\numberline {V}Relation between quadrupolar polarization and applied field gradient}{8}{}}
38 \newlabel{eq:20}{{32}{8}{}{}{}}
39 \newlabel{quadRadial}{{33}{8}{}{}{}}
40 \newlabel{eq:23}{{34}{8}{}{}{}}
41 \newlabel{eq:22}{{35}{9}{}{}{}}
42 \newlabel{eq:21}{{36}{9}{}{}{}}
43 \newlabel{eq:22}{{37}{9}{}{}{}}
44 \newlabel{eq:24}{{38}{9}{}{}{}}
45 \newlabel{eq:25}{{39}{9}{}{}{}}
46 \newlabel{eq:26}{{40}{9}{}{}{}}
47 \newlabel{eq:27}{{41}{10}{}{}{}}
48 \newlabel{eq:28}{{42}{10}{}{}{}}
49 \newlabel{eq:29}{{43}{10}{}{}{}}
50 \@writefile{toc}{\contentsline {section}{\numberline {VI}The effective dielectric constant of a quadrupolar fluid}{10}{}}
51 \newlabel{eq:31}{{46}{10}{}{}{}}
52 \newlabel{eq:32}{{47}{10}{}{}{}}
53 \newlabel{eq:33}{{48}{11}{}{}{}}
54 \newlabel{eq:34}{{49}{11}{}{}{}}
55 \newlabel{eq:36}{{50}{11}{}{}{}}
56 \@writefile{toc}{\appendix }
57 \@writefile{toc}{\contentsline {section}{\numberline {A}Point-multipolar interactions with a spatially-varying electric field}{12}{}}
58 \newlabel{eq:charge}{{A1}{12}{}{}{}}
59 \newlabel{eq:dipole}{{A2}{12}{}{}{}}
60 \newlabel{eq:quadrupole}{{A3}{12}{}{}{}}
61 \citation{Torres-del-Castillo:2006uo}
62 \citation{Smith98}
63 \@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces Potential energy $(U)$, force $(\mathbf {F})$, and torque $(\mathbf {\tau })$ expressions for a multipolar site embedded in an electric field with spatial variations, $\mathbf {E}(\mathbf {r})$. }}{13}{}}
64 \newlabel{tab:UFT}{{II}{13}{}{}{}}
65 \newlabel{eq:matrixCross}{{A10}{13}{}{}{}}
66 \@writefile{toc}{\contentsline {section}{\numberline {B}Gradient of the field due to quadrupolar polarization}{13}{}}
67 \newlabel{singular}{{B}{13}{}{}{}}
68 \newlabel{eq:8}{{B1}{13}{}{}{}}
69 \newlabel{eq:9}{{B2}{14}{}{}{}}
70 \newlabel{eq:10}{{B3}{14}{}{}{}}
71 \newlabel{eq:11}{{B4}{14}{}{}{}}
72 \newlabel{eq:12}{{B5}{14}{}{}{}}
73 \newlabel{eq:13}{{B6}{14}{}{}{}}
74 \newlabel{eq:14}{{B7}{14}{}{}{}}
75 \newlabel{eq:15}{{B8}{14}{}{}{}}
76 \newlabel{eq:16}{{B9}{15}{}{}{}}
77 \newlabel{eq:17}{{B10}{15}{}{}{}}
78 \newlabel{eq:18}{{B11}{15}{}{}{}}
79 \newlabel{eq:19}{{B12}{15}{}{}{}}
80 \bibdata{dielectricNotes,multipole}
81 \bibcite{Wolf99}{{1}{1999}{{Wolf\ \emph {et~al.}}}{{Wolf, Keblinski, Phillpot,\ and\ Eggebrecht}}}
82 \bibcite{Zahn02}{{2}{2002}{{Zahn, Schilling,\ and\ Kast}}{{}}}
83 \bibcite{Kast03}{{3}{2003}{{Kast, Schmidt,\ and\ Schilling}}{{}}}
84 \bibcite{Beckd.A.C._Bi0486381}{{4}{2005}{{Beck, Armen,\ and\ Daggett}}{{}}}
85 \bibcite{Ma05}{{5}{2005}{{Ma\ and\ Garofalini}}{{}}}
86 \bibcite{Fennell06}{{6}{2006}{{Fennell\ and\ Gezelter}}{{}}}
87 \bibcite{Allen:1989fp}{{7}{1989}{{Allen\ and\ Tildesley}}{{}}}
88 \bibcite{Neumann:1983mz}{{8}{1983}{{Neumann}}{{}}}
89 \bibcite{Neumann:1983yq}{{9}{1983}{{Neumann\ and\ Steinhauser}}{{}}}
90 \bibcite{Neumann84}{{10}{1984}{{Neumann, Steinhauser,\ and\ Pawley}}{{}}}
91 \bibcite{Neumann85}{{11}{1985}{{Neumann}}{{}}}
92 \bibcite{Horn04}{{12}{2004}{{Horn\ \emph {et~al.}}}{{Horn, Swope, Pitera, Madura, Dick, Hura,\ and\ Head-Gordon}}}
93 \bibcite{Izvekov:2008wo}{{13}{2008}{{Izvekov, Swanson,\ and\ Voth}}{{}}}
94 \bibcite{Adams:1980rt}{{14}{1980}{{Adams}}{{}}}
95 \bibcite{Adams:1981fr}{{15}{1981}{{Adams\ and\ Adams}}{{}}}
96 \bibcite{Torres-del-Castillo:2006uo}{{16}{2006}{{Torres~del Castillo\ and\ M\'{e}ndez~Garrido}}{{}}}
97 \bibcite{Smith98}{{17}{1998}{{Smith}}{{}}}
98 \bibstyle{aipnum4-1}
99 \citation{REVTEX41Control}
100 \citation{aip41Control}
101 \@writefile{toc}{\contentsline {section}{\numberline {}References}{16}{}}
102 \newlabel{LastBibItem}{{17}{16}{}{}{}}
103 \newlabel{LastPage}{{}{16}{}{}{}}