Abstract
In electrostatic embedding mixed quantum and molecular mechanics (QM/MM) approaches, the QM charge distribution is polarized by the electrostatic interaction with the MM environment. Analytic derivatives of expectation values of operators are required to extract properties such as vibrational spectra. These derivatives usually require solving a set of coupled perturbed equations for each nucleus/atom in the system, thus becoming prohibitive when the MM subsystem contains thousands of atoms. In the context of Electrostatic Potential Fitting (ESPF) QM/MM, we can easily overcome this bottleneck by defining a set of auxiliary coupled perturbed equations called the Q-vector equations. The Q-vector method scales only with the size of the QM subsystem, producing an effective charge tensor that leads to the atomic charge derivative after contraction with the MM electrostatic potential gradient. As an example, we use the charge derivatives as an analysis tool to identify the most important chromophore-polarizing amino-acids in plant cryptochrome. This finding opens up the route of defining polarizable force fields and simulating vibrational spectroscopy using ESPF QM/MM electrostatic embedding at an affordable computational cost.
Highlights
In which ZA is the nuclear charge of the QM atom A, φA is the classical external potential felt by the QM atom, and Qμν,A is the atomic charge operator.[5]
We focus on the QM atomic charge derivatives using density matrices derived from single determinant mean-field wavefunctions, in which the density matrix elements Pμν are given by
We have shown to this point that the first derivative of the Electrostatic Potential Fitted (ESPF) atomic charges with respect to MM perturbations of singledeterminant wavefunctions does not require the solution of 3 ⋅ NMM
Summary
⎠A in which ZA is the nuclear charge of the QM atom A, φA is the classical external potential felt by the QM atom, and Qμν,A is the atomic charge operator.[5]. The expression for the first derivative of the atomic charge with respect to a QM atom is given by qxA = ∑ (PμxνQμν,A + PμνQxμν,A), (6) In the case of QM atoms, this requires solving the coupled perturbed self-consistent field (CPSCF) equation 3NQM times.
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