Incorporation of charge transfer into the explicit polarization fragment method by grand canonical density functional theory

Abstract

Molecular fragmentation algorithms provide a powerful approach to extending electronic structure methods to very large systems. Here we present a method for including charge transfer between molecular fragments in the explicit polarization (X-Pol) fragment method for calculating potential energy surfaces. In the conventional X-Pol method, the total charge of each fragment is preserved, and charge transfer between fragments is not allowed. The description of charge transfer is made possible by treating each fragment as an open system with respect to the number of electrons. To achieve this, we applied Mermin's finite temperature method to the X-Pol wave function. In the application of this method to X-Pol, the fragments are open systems that partially equilibrate their number of electrons through a quasithermodynamics electron reservoir. The number of electrons in a given fragment can take a fractional value, and the electrons of each fragment obey the Fermi-Dirac distribution. The equilibrium state for the electrons is determined by electronegativity equalization with conservation of the total number of electrons. The amount of charge transfer is controlled by re-interpreting the temperature parameter in the Fermi-Dirac distribution function as a coupling strength parameter. We determined this coupling parameter so as to reproduce the charge transfer energy obtained by block localized energy decomposition analysis. We apply the new method to ten systems, and we show that it can yield reasonable approximations to potential energy profiles, to charge transfer stabilization energies, and to the direction and amount of charge transferred.

Optimization of the explicit polarization (X-Pol) potential using a hybrid density functional

“…If the specific description of charge transfer effects is important for a given problem, the fragment partitions need to be assigned in such a way that the electron donor and acceptor groups are both included in the same fragment. Alternatively, resonance charge delocalization effects can be modeled by the multiconfigurational, generalized X-Pol (GX-Pol) theory highlighted recently [47, 53] or by using ensemble DFT [16]. Here, however, we tested the simpler approach in which charge transfer is only implicit.…”

“…In this regard, one can treat all fragments by using the same method, or by mixing different electronic structure methods for different fragments (for example, MP2 for one fragment and DFT for all other fragments). Because a large system is partitioned into fragments, the X-Pol method can be made to scale well for fast calculations, and therefore, it can be used to establish a framework for the development of a next-generation force field [4] that goes beyond the conventional molecular mechanics by explicitly including a quantum mechanical treatment of electronic polarization and possibly charge transfer effects (which can be included, for example, by a recently proposed method [16] involving ensemble DFT). When X-Pol is used as a force field, we introduce a set of empirical terms to account for the missing exchange repulsion [17] and dispersion-like attractive, noncovalent interactions.…”

Classical Electrostatics for Biomolecular Simulations

“…Application of the GC-X-Pol to ten molecular complexes showed that the CT energy from this approach follows the trend of the BLW results. 394 Khaliullin et al reported a study on water dimer and other complexes using the absolutely localized molecular orbitals energy decomposition (ALMO-ED) scheme. 395 It was found that, unlike the polarization energy, the CT energy was sensitive to the water dimer orientation (flap angle).…”

Multilevel X-Pol: A Fragment-Based Method with Mixed Quantum Mechanical Representations of Different Fragments

“…The strict block localization of molecular orbitals within individual monomers in X-Pol does not allow charge delocalization between different fragments (unless one uses a grand canonical formulation, which is not employed here). 31 At distances longer than hydrogen bonding range, it is often a good approximation to neglect charge transfer, and interfragment electrostatic interactions can then be adequately described by the electrostatic embedding scheme 43–44 using the Coulomb potential (eq 5). However, at short interfragment distances where there is significant orbital overlap, one needs to take into account the energy component due to charge delocalization (sometimes also called charge transfer).…”

“…However, at short interfragment distances where there is significant orbital overlap, one needs to take into account the energy component due to charge delocalization (sometimes also called charge transfer). 30–31,61 In the present work, we account for charge transfer only empirically, in particular (in the spirit often used in molecular mechanics) 62 by modeling the charge delocalization energy with enhanced electrostatic polarization. Consequently, the electrostatic potential ${\mathrm{normal\Phi }}_{\mathrm{normalE}}^B({\mathrm{boldr}}_x^A)$ in eq 5 is recognized as an effective potential that mimics both long-range Coulomb (electrostatic) interactions and short-range charge delocalization contributions, and this can be achieved to some extent by optimizing the parameters in the $E_{\text{italicAB}}^{\text{XD}}$ term (eq 7) and possibly the charge model 63 $\{q_b^B[{\rho }_{\text{italicele}}^B]\}$ (eq 5) to best reproduce hydrogen bonding interactions for a set of bimolecular complexes 38 (however such optimization is beyond the scope of the present article).…”