Molecular electrostatic potential at the atomic sites in the effective core potential approximation

Abstract

Considering calculations of the molecular electrostatic potential at the atomic sites (MEP@AS) in the presence of effective core potentials (ECP), we found that the consequent use of the definition of MEP@AS based on the energy derivative with respect to nuclear charge leads to a formula that differs by one term from the result of simple application of Coulomb's law. We have developed a general method to analytically treat derivatives of ECP with respect to nuclear charge. Benchmarking calculations performed on a set of simple molecules show that our formula leads to a systematic decrease in the error connected with the introduction of ECP when compared to all-electron results. Because of a straightforward implementation and relatively low costs of the developed procedure we suggest to use it by default.

Exploring Chemical Space with the Alchemical Derivatives

“…We concentrate on the stability of the transmutation products, where the term “transmutation” means the change of the nuclear charge at an atomic site. Our interest is restricted only to molecules containing first and second row atoms, but the alchemical calculation scheme is also applicable for systems where the effective core potential approximation is used . As illustrative transmutations showing the potential of the method in exploring chemical space, we present some examples of increasing complexity starting with the deprotonation, continuing with the transmutation of the nitrogen molecule, and ending with the substitution of isoelectronic B–N units for C–C units and N units for C–H units in carbocyclic systems.…”

Exploring Chemical Space with Alchemical Derivatives: BN-Simultaneous Substitution Patterns in C60

“…20,37 It is also applicable for systems where the effective core potential approximation is used. 48 It was shown that on the basis of only a single SCF type calculation and the corresponding alchemical derivatives of the reference molecule, the CCS of first neighbors − implying changes in nuclear charge of ±1 − could be fully explored by simple arithmetic operations at negligible supplementary cost to a SCF calculation. As illustrative transmutations showing the potential of the CP method, some examples of increasing complexity were presented, 37 starting with the deprotonation of small molecular systems with one and more hydrogen atoms, continuing with the transmutation of the nitrogen molecule, and ending with the substitution of isoelectronic (B,N) units for (C,C) units and N units for C−H units in carbocyclic systems.…”

“…the derivatives of the density with respect to nuclear position or the nuclear charge. These derivatives can be calculated using the coupled perturbed (CP) scheme, which constitutes a powerful technique for the calculation of molecular response properties involving electric, magnetic, and geometric perturbations. − This scheme was also successfully used in calculations of the relaxation effect due to the change in the electron number, − the second and the third order derivatives with respect to nuclear charges. , It is also applicable for systems where the effective core potential approximation is used …”