Extending the definition of atomic basis sets to atoms with fractional nuclear charge.

Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a non-physical system in which an atom possess a non-integer nuclear charge. A correct quantum mechanical treatment of these systems is limited by the fact that finite size atomic basis sets do not define exponents and contraction coefficients for fractional charge atoms. This paper proposes a solution to this problem and shows that a smooth interpolation of the atomic orbital coefficients and exponents across the periodic table is a convenient way to produce accurate alchemical predictions, even using small size basis sets.

Molecular Hessian matrices from a machine learning random forest regression algorithm.

In this article, we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal coordinates are learned individually. The internal coordinates together with their specific representation guarantee rotational and translational invariance. The model is trained on a subset of the QM7 dataset but is shown to be applicable to larger molecules picked from the QM9 dataset. From the predicted Hessian, it is also possible to obtain reasonable estimates of the vibrational frequencies, normal modes, and zero point energies of the molecules.

Alchemical geometry relaxation.

We propose the relaxation of geometries throughout chemical compound space using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schrödinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both nuclear charges and nuclear positions (named "alchemical force") within the restricted Hartree-Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analyzed the convergence of the alchemical force perturbation series as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton-Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH4, NH3, H2O, and HF yield mean absolute errors of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 bohr for fourth order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree-Fock derivative for benzene, we provide numerical predictions of equilibrium energies and relaxed structures of all 17 iso-electronic charge-neutral BN-doped mutants with averaged absolute deviations of ∼27 mHa and ∼0.12 bohr, respectively.

Effects of perturbation order and basis set on alchemical predictions.

Alchemical perturbation density functional theory has been shown to be an efficient and computationally inexpensive way to explore chemical compound space. We investigate approximations made, in terms of atomic basis sets and the perturbation order, introduce an electron-density based estimate of errors of the alchemical prediction, and propose a correction for effects due to basis set incompleteness. Our numerical analysis of potential energy estimates, and resulting binding curves, is based on coupled-cluster single double (CCSD) reference results and is limited to all neutral diatomics with 14 electrons (AlH⋯NN). The method predicts binding energy, equilibrium distance, and vibrational frequencies of neighboring out-of-sample diatomics with near CCSD quality using perturbations up to the fifth order. We also discuss simultaneous alchemical mutations at multiple sites in benzene.

Role of Gln222 in Photoswitching of Aequorea Fluorescent Proteins: A Twisting and H-Bonding Affair?

Reversibly photoswitchable fluorescent proteins (RSFPs) admirably combine the genetic encoding of fluorescence with the ability to repeatedly toggle between a bright and dark state, adding a new temporal dimension to the fluorescence signal. Accordingly, in recent years RSFPs have paved the way to novel applications in cell imaging that rely on their reversible photoswitching, including many super-resolution techniques such as F-PALM, RESOLFT, and SOFI that provide nanoscale pictures of the living matter. Yet many RSFPs have been engineered by a rational approach only to a limited extent, in the absence of clear structure-property relationships that in most cases make anecdotic the emergence of the photoswitching. We reported [ Bizzarri et al. J. Am Chem Soc. 2010 , 102 , 85 ] how the E222Q replacement is a single photoswitching mutation, since it restores the intrinsic cis-trans photoisomerization properties of the chromophore in otherwise nonswitchable Aequorea proteins of different color and mutation pattern (Q-RSFPs). We here investigate the subtle role of Q222 on the excited-state photophysics of the two simplest Q-RSFPs by a combined experimental and theoretical approach, using their nonswitchable anacestor EGFP as benchmark. Our findings link indissolubly photoswitching and Q222 presence, by a simple yet elegant scenario: largely twisted chromophore structures around the double bond (including hula-twist configurations) are uniquely stabilized by Q222 via H-bonds. Likely, these H-bonds subtly modulate the electronic properties of the chromophore, enabling the conical intersection that connects the excited cis to ground trans chromophore. Thus, Q222 belongs to a restricted family of single mutations that change dramatically the functional phenotype of a protein. The capability to distinguish quantitatively T65S/E222Q EGFP ("WildQ", wQ) from the spectrally identical EGFP by quantitative Optical Lock-In Detection (qOLID) witnesses the relevance of this mutation for cell imaging.