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The SURF program allows for the calculation of the potential energy surface around a reference structure as required for the calculation of anharmonic frequencies (see the VSCF and VCI programs). The reference structure is supposed to be a (local) minimum or a transition state of a double-minimum potential. The potential is represented by energy grid points rather than an analytical representation. Within the SURF program the potential energy surface is expanded in terms of normal coordinates, linear combination of normal coordinates or localized normal coordinates. Consequently, a harmonic frequency calculation needs to be performed first. The potential will then be represented by a multi-mode expansion, i.e. a hierarchical scheme given by

V(q_1,\dots,q_{3N-6}) = \sum_i V_i(q_i) + \sum_{i<j} V_{ij}(q_i,q_j) + \sum_{i<j<k} V_{ijk}(q_i,q_j,q_k) + \dots
\end{displaymath} (58)

$\displaystyle V_i(q_i)$ $\textstyle =$ $\displaystyle V_i^0(q_i) - V(0)$ (59)
$\displaystyle V_{ij}(q_i,q_j)$ $\textstyle =$ $\displaystyle V_{ij}^0(q_i,q_j) - \sum_{r\in\{i,j\}} V_r(q_r) - V(0)$ (60)
$\displaystyle V_{ijk}(q_i,q_j,q_k)$ $\textstyle =$ $\displaystyle V_{ijk}^0(q_i,q_j,q_k) - \sum_{\stackrel{\scriptstyle r,s\in\{i,j,k\}}{r>s}} V_{rs}(q_r,q_s) - \sum_{r\in\{i,j,k\}} V_r(q_r) - V(0) \qquad$ (61)
$\displaystyle V_{ijkl}(q_i,q_j,q_k,q_l)$ $\textstyle =$ $\displaystyle \dots$ (62)

where $q_i$ denotes the coordinates. This expansion needs to be terminated after an $n$-body contribution as controlled by the keyword NDIM. The SURF program is fully parallelized in a sense that the calculation of different grid points is send to different processors (embarassingly parallel MPPX scheme). The START1D keyword is mandatory and defines the label where to jump in the input in order to do an electronic structure calculation which is terminated by the SURF command. This way the quality of the potential energy surface is defined. For example, the input for the calculation of a CCSD surface looks like:


The SURF program is based on an iterative algorithm, i.e. grid points will be added automatically to the grid representation of the potential until a convergence threshold will be met. This guarantees a well-balanced description of the different terms in the expansion of the potential and simultaneously minimizes the number of ab initio calculations for a representation of the potential. For further details see:

G. Rauhut, Efficient Calculation of Potential Energy Surfaces for the Generation of Vibrational Wave Functions, J. Chem. Phys. 121, 9313 (2004).
T. Hrenar, H.-J. Werner, G. Rauhut Accurate Calculation of Anharmonic Vibrational Frequencies of Medium Sized Molecules Using Local Coupled Cluster Methods, J. Chem. Phys. 126, 134108 (2007).


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