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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html1542"
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HREF="node29.html#SECTION002910000000000000000">27.1 <TT>VECTORS</TT> -- input of MO vectors for ET reactant and product states</A>
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<LI><A NAME="tex2html1543"
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HREF="node29.html#SECTION002920000000000000000">27.2 <TT>FOCK/NOFOCK</TT> -- method for calculating the two-electron contribution to <IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$"> </A>
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<LI><A NAME="tex2html1544"
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HREF="node29.html#SECTION002930000000000000000">27.3 <TT>TOL2E</TT> -- integral screening threshold</A>
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<LI><A NAME="tex2html1545"
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HREF="node29.html#SECTION002940000000000000000">27.4 <TT>Example</TT></A>
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<HR>
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<H1><A NAME="SECTION002900000000000000000">
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27. Electron Transfer Calculations with ET</A>
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</H1>
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<A NAME="sec:etrans"></A>
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<P>
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The NWChem electron transfer (ET) module calculates the electronic coupling energy (also called the electron transfer
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matrix element) between ET reactant and product states. The electronic coupling (<IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$">), activation energy (<IMG
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WIDTH="37" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img184.gif"
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ALT="$\Delta G^{*}$">),
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and nuclear reorganization energy (<IMG
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WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img185.gif"
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ALT="$\lambda$">) are all components of the electron transfer rate defined by Marcus' theory, which
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also depends on the temperature (reference 1):
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<P>
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<BR>
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<DIV ALIGN="RIGHT">
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<!-- MATH
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\begin{equation}
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{k_{ET}}=
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\frac{2\pi}{\hbar}
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V_{RP}^{2}
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\frac{1}{\sqrt{4\pi \lambda k_{B}T}}
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\exp \left( \frac{- \Delta G^{*}}{k_{B} T} \right)
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\end{equation}
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-->
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<TABLE WIDTH="100%" ALIGN="CENTER">
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<TR VALIGN="MIDDLE"><TD NOWRAP><IMG
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WIDTH="275" HEIGHT="85" BORDER="0"
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SRC="img186.gif"
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ALT="\begin{displaymath}
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{k_{ET}}=
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\frac{2\pi}{\hbar}
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V_{RP}^{2}
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\frac{1}{\sqrt{4\pi ...
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...da k_{B}T}}
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\exp \left( \frac{- \Delta G^{*}}{k_{B} T} \right)
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\end{displaymath}"></TD>
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<TD WIDTH=10 ALIGN="RIGHT">
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(27.1)</TD></TR>
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</TABLE>
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<BR CLEAR="ALL"></DIV><P></P>
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<P>
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The ET module utilizes the method of <EM>Corresponding Orbital Transformation</EM> to calculate <IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$">.
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The only input required are the names
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of the files containing the open-shell (UHF or ODFT) MO vectors for the ET reactant and product states (<IMG
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WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img187.gif"
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ALT="$R$"> and <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img188.gif"
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ALT="$P$">).
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<P>
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Although open-shell DFT orbitals can be used as input, the current implementation of the ET module uses a Hartree-Fock
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formalism (ref.3). Therefore, for consistency, UHF orbitals should be used for the calculation of <IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$">, although this
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is not required.
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<P>
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The basis set used in the calculation of <IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$"> must be the same as the basis set used to calculate the MO vectors of
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<IMG
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WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img187.gif"
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ALT="$R$"> and <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img188.gif"
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ALT="$P$">. The magnitude of <IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$"> depends on the amount of overlap between <IMG
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WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img187.gif"
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ALT="$R$"> and <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img188.gif"
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ALT="$P$">,
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which is important to consider when choosing the basis set. Diffuse functions may be
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necessary to fill in the overlap, particularly when the ET distance is long.
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<P>
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The MO's of <IMG
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WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img187.gif"
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ALT="$R$"> and <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img188.gif"
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ALT="$P$"> must correspond to localized states. for instance, in the reaction <IMG
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WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img189.gif"
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ALT="$A^{ -}$"> <IMG
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WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img190.gif"
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ALT="$B$"> <IMG
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WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img3.gif"
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ALT="$\rightarrow $"> <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img36.gif"
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ALT="$A$"> <IMG
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WIDTH="28" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img191.gif"
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ALT="$B^{ -}$">
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the transferring electron is localized on A in the reactant state and is localized on B in the product state.
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To verify the localization of the electron in the calculation of the vectors, carefully examine the Mulliken population
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analysis. In order to determine which orbitals are involved in the electron transfer, use the print keyword <code>"mulliken ao"</code>
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which prints the Mulliken population of each basis function.
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<P>
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An effective core potential (ECP) basis can be used to replace core electrons. However, there is one caveat: the orbitals
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involved in electron transfer must not be replaced with ECP's. Since the ET orbitals are valence orbitals, this is not usually
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a problem, but the user should use ECP's with care.
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<P>
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Suggested references are listed below. The first two references gives a good description
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of Marcus' two-state ET model, and the appendix of the third reference details the method used
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in the ET module.
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<P>
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<OL>
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<LI>R.A. Marcus, N. Sutin, Biochimica Biophysica Acta 35, 437, (1985).
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</LI>
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<LI>J.R. Bolton, N. Mataga, and G. McLendon in ``Electron Transfer in Inorganic, Organic and Biological Systems"
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(American Chemical Society, Washington, D.C., 1991)
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</LI>
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<LI>A. Farazdel, M. Dupuis, E. Clementi, and A. Aviram,
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J. Am. Chem. Soc., 112, 4206 (1990).
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</LI>
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</OL>
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<P>
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<H1><A NAME="SECTION002910000000000000000"></A>
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<A NAME="sec:etransvectors"></A>
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<BR>
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27.1 <TT>VECTORS</TT> -- input of MO vectors for ET reactant and product states
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</H1>
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<P>
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<PRE>
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VECTORS [reactants] <string reactants_filename>
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VECTORS [products ] <string products_filename>
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</PRE>
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<P>
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In the <code>VECTORS</code> directive the user specifies the source
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of the molecular orbital vectors for the ET reactant and product states.
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This is required input, as no default filename will be set by the program.
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In fact, this is the only required input in the ET module, although there are
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other optional keywords described below.
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<P>
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<H1><A NAME="SECTION002920000000000000000"></A>
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<A NAME="sec:etransfock"></A>
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<BR>
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27.2 <TT>FOCK/NOFOCK</TT> -- method for calculating the two-electron contribution to <IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$">
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</H1>
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<P>
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<PRE>
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<string (FOCK||NOFOCK) default FOCK>
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</PRE>
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<P>
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This directive enables/disables the use of the NWChem's Fock matrix
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routine in the calculation of the two-electron portion of the ET Hamiltonian.
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Since the Fock matrix routine has been optimized for speed, accuracy and parallel performance,
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it is the most efficient choice.
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<P>
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Alternatively, the user can calculate the two-electron contribution to the ET Hamiltonian
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with another subroutine which may be more accurate for systems with a small
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number of basis functions, although it is slower.
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<P>
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<H1><A NAME="SECTION002930000000000000000"></A>
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<A NAME="sec:etranstol2e"></A>
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<BR>
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27.3 <TT>TOL2E</TT> -- integral screening threshold
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</H1>
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<P>
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<PRE>
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TOL2E <real tol2e default max(10e-12,min(10e-7, S(RP)*10e-7 )>
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</PRE>
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<P>
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The variable <code>tol2e</code> is used in determining the integral
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screening threshold for the evaluation of the two-electron contribution to the Hamiltonian
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between the electron transfer reactant and product states.
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As a default, <code>tol2e</code> is set depending on the magnitude
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of the overlap between the ET reactant and product states (<IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img192.gif"
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ALT="$S_{RP}$">), and is not less than 1.0d-12
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or greater than 1.0d-7.
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<P>
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The input to specify the threshold explicitly within the <code>ET</code>
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directive is, for example:
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<P>
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<PRE>
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tol2e 1e-9
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</PRE>
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<P>
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<H1><A NAME="SECTION002940000000000000000">
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27.4 <TT>Example</TT></A>
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</H1>
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<P>
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The following example is for a simple electron transfer reaction, <IMG
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WIDTH="27" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img193.gif"
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ALT="$He_{}$"> <IMG
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WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img3.gif"
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ALT="$\rightarrow $"> <IMG
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WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img194.gif"
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ALT="$He^{ +}$">.
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The ET calculation is easy to execute, but it is crucial that ET reactant and product
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wavefunctions reflect <EM>localized states</EM>. This can be accomplished
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using either a fragment guess (shown in the example, see <A HREF="node12.html#sec:fragguess">10.5.1</A>), or a charged atomic
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density guess (see <A HREF="node12.html#sec:atomscf">10.5.2</A>).
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For self-exchange ET reactions such as this one, you can use the
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<code>REORDER</code> keyword to move the electron from the first helium to the second (see <A HREF="node12.html#sec:vectors">10.5</A>).
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<P>
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Example input :
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<PRE>
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#ET reactants:
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charge 1
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scf
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doublet; uhf; vectors input fragment HeP.mo He.mo output HeA.mo
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# HeP.mo are the vectors for He(+),
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# He.mo are the vectors for neutral He.
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end
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task scf
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#ET products:
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charge 1
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scf
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doublet; uhf; vectors input HeA.mo reorder 2 1 output HeB.mo
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end
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task scf
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et
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vectors reactants HeA.mo
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vectors products HeB.mo
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end
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task scf et
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</PRE>
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<P>
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Here is what the output looks like for this example:
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<PRE>
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Electron Transfer Calculation
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-----------------------------
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MO vectors for reactants: HeA.mo
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MO vectors for products : HeB.mo
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Electronic energy of reactants H(RR) -5.3402392824
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Electronic energy of products H(PP) -5.3402392824
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Reactants/Products overlap S(RP) -0.0006033839
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Reactants/Products interaction energy:
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-------------------------------------
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One-electron contribution H1(RP) 0.0040314092
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Beginning calculation of 2e contribution
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Two-electron integral screening (tol2e) : 6.03E-11
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Two-electron contribution H2(RP) -0.0007837138
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Total interaction energy H(RP) 0.0032476955
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Electron Transfer Coupling Energy |V(RP)| 0.0000254810
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5.592 cm-1
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0.000693 eV
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0.016 kcal/mol
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</PRE>
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<P>
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The overlap between the ET reactant and product states (<IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img192.gif"
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ALT="$S_{RP}$">) is small,
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so the magnitude of the coupling between the states is also small.
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If the fragment guess
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or charged atomic density guess were not used, the Mulliken spin population would be 0.5 on both He atoms, the overlap between
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the ET reactant and product states would be <code>100 %</code> and an infinite
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<IMG
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WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img4.gif"
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ALT="$V_{RP}$"> would result.
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<P>
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<ADDRESS>
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Edoardo Apra
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2004-05-25
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