Empirical Energy Functions

Empirical energy functions describe the energy of the molecule as a function of the atomic coordinates (Karplus and Petsko, 1990; Némethy, Pottie, and Scheraga, 1983; Lifson and Stern, 1982; Brooks et al., 1983; Weiner et al., 1984; Burkert and Allinger, 1982). Most of today's empirical energy functions contain conformational and nonbonded interaction energy terms involving sets of two, three, and four atoms. A harmonic approximation is used to account for deformations in bond length and angles. Four-atom terms are used for torsion potentials. Two-atom terms are employed for the nonbonded interactions. A variety of specific parameterizations for empirical energy functions are available in X-PLOR (Section 3.6).

XPLOR's empirical energy function has the general form

$$E_{EMPIRICAL} = \sum_{p=1}^{N} [ w^p_{BOND} E_{BOND} + w^p_{ANGL} E_{ANGL} +$$

$$w^p_{DIHE} E_{DIHE} + w^p_{IMPR} E_{IMPR} +$$

$$w^p_{VDW} E_{VDW} + w^p_{ELEC} E_{ELEC} +$$

$$w^p_{PVDW} E_{PVDW} + w^p_{PELE} E_{PELE} +$$

$$w^p_{HBON} E_{HBON} ].$$ (4.3)

The sum is carried out over all double selections of atoms (see Section 4.7) with weights $w^p_n$. The default for the double selections is one double selection involving all atoms with unity weights. The first four terms in Eq. 4.3 are conformational energy terms.

The remaining five terms in Eq. 4.3 describe nonbonded interactions. The term $E_{VDW}$ describes the non-symmetry-related van der Waals energy, $E_{ELEC}$ describes the non-symmetry-related electrostatic energy, $E_{PVDW}$ describes the van der Waals energy between symmetry-related atoms, and $E_{PELE}$ describes the symmetry-related electrostatic energy. The term $E_{HBON}$ describes an explicit hydrogen-bonding energy. This term is used only in older parameter files.

In the next sections, the empirical energy terms are described in more detail.