43 POTENTIAL ENERGY SURFACES (SURF)

SURF,Start1D=label1,options

The SURF program allows for the calculation of the potential energy surface around the equilibrium structure as required for the calculation of anharmonic frequencies (see the VSCF and VCI programs). Currently the program is limited to the case of one minimum. The potential is represented by energy grid points rather than a Taylor expansion. Within the SURF the potential energy surfaces is expanded in terms of normal coordinates. Consequently, a harmonic frequency calculation needs to be performed first. The potential will then be represented by a hierarchical scheme given by

$$V(q_1,\dots,q_{3N-6}) = \sum_i V_i(q_i) + \sum_{i<j} V_{ij}(q_i,q_j) + \sum_{i<j<k} V_{ijk}(q_i,q_j,q_k) + \dots$$ (15)

with

$$V_i(q_i) = V_i^0(q_i) - V(0)$$ (16)

$$V_{ij}(q_i,q_j) = V_{ij}^0(q_i,q_j) - \sum_{r\in\{i,j\}} V_r(q_r) - V(0)$$ (17)

$$V_{ijk}(q_i,q_j,q_k) = V_{ijk}^0(q_i,q_j,q_k) - \sum_{\stackrel{\scriptstyle r,s\in\{i,j,k\}}{r>s}} V_{rs}(q_r,q_s) - \sum_{r\in\{i,j,k\}} V_r(q_r) - V(0) \qquad$$ (18)

$$V_{ijkl}(q_i,q_j,q_k,q_l) = \dots$$ (19)

where $q_i$ denotes the normal 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 (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.

label1                         
hf                            
ccsd                         
surf,start1D=label1

The SURF program is based on a 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).