1% 2% $Id$ 3% 4\label{sec:etrans} 5 6The NWChem electron transfer (ET) module calculates the electronic coupling energy (also called the electron transfer 7matrix element) between ET reactant and product states. The electronic coupling ($V_{RP}$), activation energy ($\Delta G^{*}$), 8and nuclear reorganization energy ($\lambda$) are all components of the electron transfer rate defined by Marcus' theory, which 9also depends on the temperature (reference 1): 10 11\begin{equation} 12{k_{ET}}= 13\frac{2\pi}{\hbar} 14V_{RP}^{2} 15\frac{1}{\sqrt{4\pi \lambda k_{B}T}} 16\exp \left( \frac{- \Delta G^{*}}{k_{B} T} \right) 17\end{equation} 18 19The ET module utilizes the method of {\em Corresponding Orbital Transformation} to calculate $V_{RP}$. 20The only input required are the names 21of the files containing the open-shell (UHF) MO vectors for the ET reactant and product states ($R$ and $P$). 22 23The basis set used in the calculation of $V_{RP}$ must be the same as the basis set used to calculate the MO vectors of 24$R$ and $P$. The magnitude of $V_{RP}$ depends on the amount of overlap between $R$ and $P$, 25which is important to consider when choosing the basis set. Diffuse functions may be 26necessary to fill in the overlap, particularly when the ET distance is long. 27 28The MO's of $R$ and $P$ must correspond to localized states. for instance, in the reaction $A^{ -}$ $B$ $\rightarrow$ $A$ $B^{ -}$ 29the transferring electron is localized on A in the reactant state and is localized on B in the product state. 30To verify the localization of the electron in the calculation of the vectors, carefully examine the Mulliken population 31analysis. In order to determine which orbitals are involved in the electron transfer, use the print keyword \verb+"mulliken ao"+ 32which prints the Mulliken population of each basis function. 33 34An effective core potential (ECP) basis can be used to replace core electrons. However, there is one caveat: the orbitals 35involved in electron transfer must not be replaced with ECP's. Since the ET orbitals are valence orbitals, this is not usually 36a problem, but the user should use ECP's with care. 37 38Suggested references are listed below. The first two references gives a good description 39of Marcus' two-state ET model, and the appendix of the third reference details the method used 40in the ET module. 41 42\begin{enumerate} 43\item R.A. Marcus, N. Sutin, Biochimica Biophysica Acta 35, 437, (1985). 44\item J.R. Bolton, N. Mataga, and G. McLendon in ``Electron Transfer in Inorganic, Organic and Biological Systems" 45(American Chemical Society, Washington, D.C., 1991) 46\item A. Farazdel, M. Dupuis, E. Clementi, and A. Aviram, 47J.~Am.~Chem.~Soc., 112, 4206 (1990). 48\end{enumerate} 49 50\section{{\tt VECTORS} --- input of MO vectors for ET reactant and product states} 51\label{sec:etransvectors} 52 53\begin{verbatim} 54 VECTORS [reactants] <string reactants_filename> 55 VECTORS [products ] <string products_filename> 56\end{verbatim} 57 58In the \verb+VECTORS+ directive the user specifies the source 59of the molecular orbital vectors for the ET reactant and product states. 60This is required input, as no default filename will be set by the program. 61In fact, this is the only required input in the ET module, although there are 62other optional keywords described below. 63 64\section{{\tt FOCK/NOFOCK} --- method for calculating the two-electron contribution to $V_{RP}$ } 65\label{sec:etransfock} 66 67 \begin{verbatim} 68 <string (FOCK||NOFOCK) default FOCK> 69 \end{verbatim} 70 71This directive enables/disables the use of the NWChem's Fock matrix 72routine in the calculation of the two-electron portion of the ET Hamiltonian. 73Since the Fock matrix routine has been optimized for speed, accuracy and parallel performance, 74it is the most efficient choice. 75 76Alternatively, the user can calculate the two-electron contribution to the ET Hamiltonian 77with another subroutine which may be more accurate for systems with a small 78number of basis functions, although it is slower. 79 80\section{{\tt TOL2E} --- integral screening threshold} 81\label{sec:etranstol2e} 82 83\begin{verbatim} 84 TOL2E <real tol2e default max(10e-12,min(10e-7, S(RP)*10e-7 )> 85\end{verbatim} 86 87The variable \verb+tol2e+ is used in determining the integral 88screening threshold for the evaluation of the two-electron contribution to the Hamiltonian 89between the electron transfer reactant and product states. 90As a default, \verb+tol2e+ is set depending on the magnitude 91of the overlap between the ET reactant and product states ($S_{RP}$), and is not less than 1.0d-12 92or greater than 1.0d-7. 93 94The input to specify the threshold explicitly within the \verb+ET+ 95directive is, for example: 96 97\begin{verbatim} 98 tol2e 1e-9 99\end{verbatim} 100 101\section{{\tt Example}} 102 103The following example is for a simple electron transfer reaction, $He_{}$ $\rightarrow$ $He^{ +}$. 104The ET calculation is easy to execute, but it is crucial that ET reactant and product 105wavefunctions reflect {\em localized states}. This can be accomplished 106using either a fragment guess (shown in the example, see \ref{sec:fragguess}), or a charged atomic 107density guess (see \ref{sec:atomscf}). 108For self-exchange ET reactions such as this one, you can use the 109\verb+REORDER+ keyword to move the electron from the first helium to the second (see \ref{sec:vectors}). 110 111Example input : 112\begin{verbatim} 113 114#ET reactants: 115charge 1 116scf 117 doublet; uhf; vectors input fragment HeP.mo He.mo output HeA.mo 118# HeP.mo are the vectors for He(+), 119# He.mo are the vectors for neutral He. 120end 121task scf 122 123#ET products: 124charge 1 125scf 126 doublet; uhf; vectors input HeA.mo reorder 2 1 output HeB.mo 127end 128task scf 129 130et 131 vectors reactants HeA.mo 132 vectors products HeB.mo 133end 134task scf et 135 136\end{verbatim} 137 138Here is what the output looks like for this example: 139\begin{verbatim} 140 Electron Transfer Calculation 141 ----------------------------- 142 143 MO vectors for reactants: HeA.mo 144 MO vectors for products : HeB.mo 145 146 Electronic energy of reactants H(RR) -5.3402392824 147 Electronic energy of products H(PP) -5.3402392824 148 149 Reactants/Products overlap S(RP) -0.0006033839 150 151 Reactants/Products interaction energy: 152 ------------------------------------- 153 One-electron contribution H1(RP) 0.0040314092 154 155 Beginning calculation of 2e contribution 156 Two-electron integral screening (tol2e) : 6.03E-11 157 158 Two-electron contribution H2(RP) -0.0007837138 159 Total interaction energy H(RP) 0.0032476955 160 161 Electron Transfer Coupling Energy |V(RP)| 0.0000254810 162 5.592 cm-1 163 0.000693 eV 164 0.016 kcal/mol 165 166\end{verbatim} 167 168The overlap between the ET reactant and product states ($S_{RP}$) is small, 169so the magnitude of the coupling between the states is also small. 170If the fragment guess 171or charged atomic density guess were not used, the Mulliken spin population would be 0.5 on both He atoms, the overlap between 172the ET reactant and product states would be \verb+100 %+ and an infinite 173$V_{RP}$ would result. 174