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root/group/trunk/multipole/dielectric_new.aux
Revision: 4353
Committed: Tue Sep 15 15:56:07 2015 UTC (8 years, 9 months ago) by mlamichh
File size: 7920 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{Zahn02,Fennell06}
9 \citation{PaperI,PaperII}
10 \citation{Kirkwood39,Onsagar36,LoganI81,LoganII82,LoganIII82}
11 \citation{Neumann83}
12 \citation{Neumann-Steinhauser83}
13 \citation{Neumann83}
14 \citation{Zahn02}
15 \citation{Izvekov:2008wo}
16 \citation{JeonI03,JeonII03,Chitanvis96}
17 \@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{2}{}}
18 \citation{Ernst92}
19 \citation{Jackson98}
20 \citation{AduGyamfi78,AduGyamfi81}
21 \@writefile{toc}{\contentsline {subsection}{\numberline {A}Boltzmann average of orientational polarization - dipole}{4}{}}
22 \newlabel{boltzAverage-dipole}{{I\tmspace +\thinmuskip {.1667em}A}{4}{}{}{}}
23 \@writefile{toc}{\contentsline {subsection}{\numberline {B}Boltzmann average of orientational polarization - quadrupole}{4}{}}
24 \newlabel{boltzQuad}{{4}{4}{}{}{}}
25 \newlabel{energyQuad}{{5}{5}{}{}{}}
26 \@writefile{toc}{\contentsline {section}{\numberline {II}External field perturbation}{5}{}}
27 \newlabel{pertDipole}{{8}{5}{}{}{}}
28 \citation{Stern03}
29 \newlabel{pertQuad}{{9}{6}{}{}{}}
30 \newlabel{sec:perturbation}{{II}{6}{}{}{}}
31 \@writefile{toc}{\contentsline {section}{\numberline {III}Fluctuation formula}{6}{}}
32 \newlabel{flucDipole}{{10}{6}{}{}{}}
33 \newlabel{flucQuad}{{12}{6}{}{}{}}
34 \newlabel{propConstQuad}{{13}{6}{}{}{}}
35 \newlabel{sec:fluctuation}{{III}{6}{}{}{}}
36 \citation{Neumann83}
37 \@writefile{toc}{\contentsline {section}{\numberline {IV}Potential of mean force}{7}{}}
38 \newlabel{sec:PMF}{{IV}{7}{}{}{}}
39 \@writefile{toc}{\contentsline {section}{\numberline {V}Correction factor}{7}{}}
40 \@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.}}{8}{}}
41 \newlabel{fig:stockmayer}{{1}{8}{}{}{}}
42 \@writefile{toc}{\contentsline {subsection}{\numberline {A}Dipolar system}{8}{}}
43 \newlabel{dipole-chargeTensor}{{17}{8}{}{}{}}
44 \newlabel{dipole-diopleTensor}{{18}{8}{}{}{}}
45 \citation{Neumann83,Jackson98}
46 \citation{Adams:1980rt,Adams:1981fr,Neumann83}
47 \citation{Adams:1980rt,Adams:1981fr,Neumann83}
48 \newlabel{constDipole}{{19}{9}{}{}{}}
49 \newlabel{singular}{{20}{9}{}{}{}}
50 \newlabel{fourierDipole}{{23}{9}{}{}{}}
51 \newlabel{correctionFormula}{{25}{9}{}{}{}}
52 \@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Expressions for the dipolar correction factor ($A$) for the real-space electrostatic methods in terms of the damping parameter ($\alpha $) and the cutoff radius ($r_c$). The Ewald-Kornfeld result derived in Refs. \rev@citealpnum {Adams:1980rt,Adams:1981fr,Neumann83} is shown for comparison using the Ewald convergence parameter ($\kappa $) and the real-space cutoff value ($r_c$). }}{10}{}}
53 \newlabel{tab:A}{{I}{10}{}{}{}}
54 \@writefile{toc}{\contentsline {subsection}{\numberline {B}Quadrupolar system}{10}{}}
55 \newlabel{gradMaxwell}{{26}{10}{}{}{}}
56 \newlabel{quadCharge}{{27}{10}{}{}{}}
57 \citation{PaperI}
58 \citation{PaperI}
59 \citation{LoganI81}
60 \newlabel{quadDip}{{28}{11}{}{}{}}
61 \newlabel{quadRadial}{{29}{11}{}{}{}}
62 \newlabel{constQaud}{{32}{11}{}{}{}}
63 \citation{Neumann83}
64 \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces With the real-space electrostatic methods, the effective quadrupolar tensor, $\mathbf {T}_{\alpha \beta \gamma \delta }(r)$, governing interactions between molecular quadrupoles can be represented by interaction of charges, point dipoles or single point quadrupoles.}}{12}{}}
65 \newlabel{fig:quadrupolarFluid}{{2}{12}{}{}{}}
66 \citation{Ernst92}
67 \newlabel{fourierQuad}{{35}{13}{}{}{}}
68 \newlabel{fourierQuad2}{{36}{13}{}{}{}}
69 \newlabel{realTensorQaud}{{37}{13}{}{}{}}
70 \newlabel{tracedConstQuad}{{38}{13}{}{}{}}
71 \@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces Expressions for the quadrupolar correction factor ($A$) for the real-space electrostatic methods in terms of the damping parameter ($\alpha $) and the cutoff radius ($r_c$). The dimension of the correction factor is $ length^{-2}$ in case of quadrupolar fluid.}}{14}{}}
72 \newlabel{tab:B}{{II}{14}{}{}{}}
73 \@writefile{toc}{\contentsline {section}{\numberline {VI}Methodology}{14}{}}
74 \@writefile{toc}{\contentsline {section}{\numberline {VII}Result}{14}{}}
75 \@writefile{toc}{\contentsline {section}{\numberline {VIII}Conclusion}{14}{}}
76 \@writefile{toc}{\appendix }
77 \@writefile{toc}{\contentsline {section}{\numberline {A}Point-multipolar interactions with a spatially-varying electric field}{15}{}}
78 \newlabel{eq:charge}{{A1}{15}{}{}{}}
79 \newlabel{eq:dipole}{{A2}{15}{}{}{}}
80 \newlabel{eq:quadrupole}{{A3}{15}{}{}{}}
81 \citation{Torres-del-Castillo:2006uo}
82 \citation{Smith98}
83 \@writefile{lot}{\contentsline {table}{\numberline {III}{\ignorespaces Potential energy $(U)$, force $(\mathbf {F})$, and torque $(\mathbf {\tau })$ expressions for a multipolar site embedded in an electric field with spatial variations, $\mathbf {E}(\mathbf {r})$. }}{16}{}}
84 \newlabel{tab:UFT}{{III}{16}{}{}{}}
85 \newlabel{eq:matrixCross}{{A10}{16}{}{}{}}
86 \@writefile{toc}{\contentsline {section}{\numberline {B}Gradient of the field due to quadrupolar polarization}{16}{}}
87 \newlabel{singularQuad}{{B}{16}{}{}{}}
88 \newlabel{eq:8}{{B1}{16}{}{}{}}
89 \newlabel{eq:9}{{B2}{17}{}{}{}}
90 \newlabel{eq:10}{{B3}{17}{}{}{}}
91 \newlabel{eq:11}{{B4}{17}{}{}{}}
92 \newlabel{eq:12}{{B5}{17}{}{}{}}
93 \newlabel{eq:13}{{B6}{17}{}{}{}}
94 \newlabel{eq:14}{{B7}{17}{}{}{}}
95 \newlabel{eq:15}{{B8}{17}{}{}{}}
96 \newlabel{eq:16}{{B9}{18}{}{}{}}
97 \newlabel{eq:17}{{B10}{18}{}{}{}}
98 \newlabel{eq:18}{{B11}{18}{}{}{}}
99 \newlabel{eq:19}{{B12}{18}{}{}{}}
100 \bibdata{dielectric_newNotes,multipole}
101 \bibcite{Wolf99}{{1}{1999}{{Wolf\ \emph {et~al.}}}{{Wolf, Keblinski, Phillpot,\ and\ Eggebrecht}}}
102 \bibcite{Zahn02}{{2}{2002}{{Zahn, Schilling,\ and\ Kast}}{{}}}
103 \bibcite{Kast03}{{3}{2003}{{Kast, Schmidt,\ and\ Schilling}}{{}}}
104 \bibcite{Beckd.A.C._Bi0486381}{{4}{2005}{{Beck, Armen,\ and\ Daggett}}{{}}}
105 \bibcite{Ma05}{{5}{2005}{{Ma\ and\ Garofalini}}{{}}}
106 \bibcite{Fennell06}{{6}{2006}{{Fennell\ and\ Gezelter}}{{}}}
107 \bibcite{PaperI}{{7}{2014}{{Lamichhane, Gezelter,\ and\ Newman}}{{}}}
108 \bibcite{PaperII}{{8}{2014}{{Lamichhane, Newman,\ and\ Gezelter}}{{}}}
109 \bibcite{Kirkwood39}{{9}{1939}{{Kirkwood}}{{}}}
110 \bibcite{Onsagar36}{{10}{1936}{{Onsager}}{{}}}
111 \bibcite{LoganI81}{{11}{1981}{{Logan}}{{}}}
112 \bibcite{LoganII82}{{12}{1982{}}{{Logan}}{{}}}
113 \bibcite{LoganIII82}{{13}{1982{}}{{Logan}}{{}}}
114 \bibcite{Neumann83}{{14}{1983}{{Neumann}}{{}}}
115 \bibcite{Neumann-Steinhauser83}{{15}{1983{}}{{Neumann\ and\ Steinhauser}}{{}}}
116 \bibcite{Izvekov:2008wo}{{16}{2008}{{Izvekov, Swanson,\ and\ Voth}}{{}}}
117 \bibcite{JeonI03}{{17}{2003{}}{{Jeon\ and\ Kim}}{{}}}
118 \bibcite{JeonII03}{{18}{2003{}}{{Jeon\ and\ Kim}}{{}}}
119 \bibcite{Chitanvis96}{{19}{1996}{{Chitanvis}}{{}}}
120 \bibcite{Ernst92}{{20}{1992}{{Ernst\ \emph {et~al.}}}{{Ernst, Wu, Liu, Nagel,\ and\ Neubert}}}
121 \bibcite{Jackson98}{{21}{1998}{{Jackson}}{{}}}
122 \bibcite{AduGyamfi78}{{22}{1978}{{Adu-Gyamfi}}{{}}}
123 \bibcite{AduGyamfi81}{{23}{1981}{{Adu-Gyamfi}}{{}}}
124 \bibcite{Stern03}{{24}{2003}{{Stern\ and\ Feller}}{{}}}
125 \bibcite{Adams:1980rt}{{25}{1980}{{Adams}}{{}}}
126 \bibcite{Adams:1981fr}{{26}{1981}{{Adams\ and\ Adams}}{{}}}
127 \bibcite{Neumann:1983yq}{{27}{1983{}}{{Neumann\ and\ Steinhauser}}{{}}}
128 \bibcite{Torres-del-Castillo:2006uo}{{28}{2006}{{Torres~del Castillo\ and\ M\'{e}ndez~Garrido}}{{}}}
129 \@writefile{toc}{\contentsline {section}{\numberline {}References}{19}{}}
130 \bibcite{Smith98}{{29}{1998}{{Smith}}{{}}}
131 \bibstyle{aipnum4-1}
132 \citation{REVTEX41Control}
133 \citation{aip41Control}
134 \newlabel{LastBibItem}{{29}{20}{}{}{}}
135 \newlabel{LastPage}{{}{20}{}{}{}}