Constrained Multipole Moment Density Functional Theory for the Frozen Contribution in Non-Covalent Complexes

The constrained dipole moment density functional theory allows one to control the magnitude and the components of the molecular dipole moment. In this work, we present a methodology which can control the dipole, quadrupole, and octupole moments in a variational and nonempirical way. This development allows us to estimate the individual (dipole, quadrupole, and octupole) and the combined (dipole-quadrupole, dipole-octupole, quadrupole-octupole, and dipole-quadrupole-octupole) multipole contributions in the formation of the ground state of the complex, taking as reference the frozen state of the complex. These contributions allow us to introduce an approximation to the variational frozen state and the corresponding frozen contribution. To test the reliability of the theoretical development, we study four sets of noncovalent complexes from the literature with a total of 24 systems. The individual and the combined multipole contributions results reveal the nature of the interaction between fragments according to these multipole moments, and the rather fast convergence of the multipole expansion, which, according to the results obtained, indicates that by including just the dipole, quadrupole, and octupole moments, one can describe the frozen state reasonably well.