J. theor. BioL (1975) 54, 389-390
The Efficient Computation of Conformational Energy Surfaces Using SCF Molecular Orbital Methods In a paper concerned with hydrogen-bonded systems, Singh & Ferro (1974) mentioned a method for decreasing the computing time required to carry out a series of CNDO/2 ~ople & Segal, 1966) calculations. We have been using what is apparently a similar method to aid our calculations of conformational energy surfaces of drug molecules. The advantages are such that it may be of more widespread interest, and the details are set out here more fully. The procedure consists essentially of using the molecular orbitals calculated for one conformation as the starting point for the following computation. Commonly, the preparation of a conformational energy surface requires calculating the energy of a molecule as a function of two dihedral angles: a 20 ° grid is often used initially and 18 x 18 = 324 points may therefore be required to define the surface. If SCF MO methods are used the amount of computation required is considerable. Further, a fine grid of perhaps 5° intervals is normally used in regions of minimum energy. Thus any method of reducing the work involved is welcome. Our technique uses the final coefficients obtained for one conformation as the basis for the calculation at the next grid point. Some examples of CNDO/2 calculations employing this procedure are given in Table 1. The calculations were made with a CNDO/2 program (Segal, 1966) with the original Pople TABLE 1
Examples of CNDO/2 calculations
Molecule
Muscimol C~HeN20a Ibotenic acid anion C6HsNaO4 ?-aminobutyric acid C~HgNOz ~-fluoro y-aminobutyric acid C~HeFNO2 4-amino tetrolic acid C4HsNOa T.a.
Time/conformation: normal calculation
(see)
Time/conformation: coefficients saved from a previous calculation (sec)
9
9 21 7
I1 9
11 7
19 35
389
25
390
D.
WARNER
AND
P . W. B O R T H W I C K
parameterization (Pople & Beveridge, 1970), implemented on a CDC 7600 computer. The figures in Table 1 refer to a grid of 20 ° with a self-consistency criterion of 0.0001 a.u. in the electronic energy. Considerable economies are sometimes possible. Using a 5 ° grid the savings are even greater. For example, with muscimol the time per conformation is reduced to 8 sec, 42 Yo o f the original value. In addition the method can be useful in cases where convergence is difficult to achieve. In the case o f ibotenic acid a CNDO/2 calculation taking the solution to the Huckel-type matrix as a starting point in the normal way, does not converge and some method, such as averaging successive Fock matrices, must be used to force convergence. In contrast, using the results from a previous conformation leads immediately to convergence with no averaging necessary and a consequent substantial saving of time as detailed in Table 1. Computationally, the method is very convenient. It does not require the intermediate storage of large arrays, and central core memory may therefore be used. Alternatively, since the saved information is accessed only once per conformation, use may be made of disc storage with little loss in efficiency. Finally it should be mentioned that there appears to be no reason why the method should not be employed with the more sophisticated SCF procedures such as INDO, N D D O and ab initio. However, in these approaches the calculation of electron repulsion integrals takes up a progressively greater fraction of the total time and savings made in the iterative part of the computation will represent a smaller percentage of the whole. We are grateful to the Science Research Council of the U.K. for awards. D. WARNER AND P. W. BORTHWICK
The Department of Physics, The City University, St John Street, London EC1 V 4PB England (Received 15 October 1974) REFERENCES POPLE, J. A. & BEVERIDCE,D. L. (1970). In Approximate Molecular Orbital Theory. New York: McGraw-Hill. POrL~, J. A. & SEPAL,G. A. (1966). J. chem. Phys. 44, 3289. SEGAL, G. A. (1966). Program 91, Quantum Chemistry Program Exchange, Indiana University. SINGH, R, D. & FERRO,D. R. (1974). J. phys. Chem. 78, 970.
The Efficient Computation of Conformational Energy Surfaces Using SCF Molecular Orbital Methods In a paper concerned with hydrogen-bonded systems, Singh & Ferro (1974) mentioned a method for decreasing the computing time required to carry out a series of CNDO/2 ~ople & Segal, 1966) calculations. We have been using what is apparently a similar method to aid our calculations of conformational energy surfaces of drug molecules. The advantages are such that it may be of more widespread interest, and the details are set out here more fully. The procedure consists essentially of using the molecular orbitals calculated for one conformation as the starting point for the following computation. Commonly, the preparation of a conformational energy surface requires calculating the energy of a molecule as a function of two dihedral angles: a 20 ° grid is often used initially and 18 x 18 = 324 points may therefore be required to define the surface. If SCF MO methods are used the amount of computation required is considerable. Further, a fine grid of perhaps 5° intervals is normally used in regions of minimum energy. Thus any method of reducing the work involved is welcome. Our technique uses the final coefficients obtained for one conformation as the basis for the calculation at the next grid point. Some examples of CNDO/2 calculations employing this procedure are given in Table 1. The calculations were made with a CNDO/2 program (Segal, 1966) with the original Pople TABLE 1
Examples of CNDO/2 calculations
Molecule
Muscimol C~HeN20a Ibotenic acid anion C6HsNaO4 ?-aminobutyric acid C~HgNOz ~-fluoro y-aminobutyric acid C~HeFNO2 4-amino tetrolic acid C4HsNOa T.a.
Time/conformation: normal calculation
(see)
Time/conformation: coefficients saved from a previous calculation (sec)
9
9 21 7
I1 9
11 7
19 35
389
25
390
D.
WARNER
AND
P . W. B O R T H W I C K
parameterization (Pople & Beveridge, 1970), implemented on a CDC 7600 computer. The figures in Table 1 refer to a grid of 20 ° with a self-consistency criterion of 0.0001 a.u. in the electronic energy. Considerable economies are sometimes possible. Using a 5 ° grid the savings are even greater. For example, with muscimol the time per conformation is reduced to 8 sec, 42 Yo o f the original value. In addition the method can be useful in cases where convergence is difficult to achieve. In the case o f ibotenic acid a CNDO/2 calculation taking the solution to the Huckel-type matrix as a starting point in the normal way, does not converge and some method, such as averaging successive Fock matrices, must be used to force convergence. In contrast, using the results from a previous conformation leads immediately to convergence with no averaging necessary and a consequent substantial saving of time as detailed in Table 1. Computationally, the method is very convenient. It does not require the intermediate storage of large arrays, and central core memory may therefore be used. Alternatively, since the saved information is accessed only once per conformation, use may be made of disc storage with little loss in efficiency. Finally it should be mentioned that there appears to be no reason why the method should not be employed with the more sophisticated SCF procedures such as INDO, N D D O and ab initio. However, in these approaches the calculation of electron repulsion integrals takes up a progressively greater fraction of the total time and savings made in the iterative part of the computation will represent a smaller percentage of the whole. We are grateful to the Science Research Council of the U.K. for awards. D. WARNER AND P. W. BORTHWICK
The Department of Physics, The City University, St John Street, London EC1 V 4PB England (Received 15 October 1974) REFERENCES POPLE, J. A. & BEVERIDCE,D. L. (1970). In Approximate Molecular Orbital Theory. New York: McGraw-Hill. POrL~, J. A. & SEPAL,G. A. (1966). J. chem. Phys. 44, 3289. SEGAL, G. A. (1966). Program 91, Quantum Chemistry Program Exchange, Indiana University. SINGH, R, D. & FERRO,D. R. (1974). J. phys. Chem. 78, 970.
