A fragment molecular-orbital–multicomponent molecular-orbital method for analyzing H∕D isotope effects in large molecules

The any particle molecular orbital/molecular mechanics approach

A computational scheme is proposed to broaden the range of applications of multicomponent methodologies for the study of local properties of big molecular systems existing in the gas phase and in solvated environments. This scheme extends the any particle molecular orbital (APMO) approach in the quantum mechanics/molecular mechanics (QM/MM) framework. As a first assessment of the performance of the proposed approach, we estimate the proton affinities (PAs) of seventy amines in the gas phase and the proton binding energies (PBEs) in the gas phase and in an explicitly solvated environment of the sixty-one protons present in the chignolin protein. These calculations are performed with the QM/MM versions of the APMO second-order proton propagator (APMO-PP2) and the APMO extended Koopmans' theorem (APMO-KT) approaches. Calculated PAs and PBEs show significant reductions in the computational effort with a reduced loss in accuracy. These results suggest that the APMO/MM scheme might be used as a low-cost multi-component alternative for studies of local properties in big molecular systems. Graphical Abstract QMMM regions and CPU times for the APMO/MM approach.

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules

An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

Interpretation of intermolecular geometric isotope effect in hydrogen bonds: nuclear orbital plus molecular orbital study

The intermolecular geometric isotope effect (GIE) in hydrogen bond A-X···B (X = H and D) is investigated theoretically using the nuclear orbital plus molecular orbital (NOMO) theory. To interpret the GIE in terms of physically meaningful energy components such as electrostatic and exchange-repulsion interactions, the reduced variational space self-consistent-field method is extended to the NOMO scheme. The intermolecular GIE is analyzed as a two-stage process: the intramolecular bond shrinkage and the intermolecular bond elongation. According to the isotopic shifts of energy components described by the NOMO/MP2 method, the intermolecular GIE is approximately interpreted as a process reducing the exchange-repulsion interaction after the decrease of electrostatic interaction.

Extending the Power of Quantum Chemistry to Large Systems with the Fragment Molecular Orbital Method

Following the brief review of the modern fragment-based methods and other approaches to perform quantum-mechanical calculations of large systems, the theoretical development of the fragment molecular orbital method (FMO) is covered in detail, with the emphasis on the physical properties, which can be computed with FMO. The FMO-based polarizable continuum model (PCM) for treating the solvent effects in large systems and the pair interaction energy decomposition analysis (PIEDA) are described in some detail, and a range of applications of FMO to biological studies is introduced. The factors determining the relative stability of polypeptide conformers (alpha-helix, beta-turn, and extended form) are elucidated using FMO/PCM and PIEDA, and the interactions in the Trp-cage miniprotein construct (PDB: 1L2Y) are analyzed using PIEDA.

Electron-electron and electron-nucleus correlation effects on exponent values of Gaussian-type functions for quantum protons and deuterons

Electron-electron and electron-nucleus correlation effects on exponent (alpha) values of Gaussian-type functions (GTFs) for quantum protons and deuterons in BH3, CH4, NH3, H2O, and HF molecular systems and their deuterated counterparts were analyzed using the second-order Moller-Plesset (MP2) level of theory of the multicomponent molecular orbital (MCMO-MP2) method. This method can simultaneously determine both nuclear and electronic wave functions. Results showed that the average alpha value (alpha(ave)) of the optimized alpha in single s-type ([1s]) GTF for a proton and a deuteron is similar to that determined using the Hartree-Fock level of the MCMO (MCMO-HF) method. In contrast, due to the electron-nucleus correlation effect, the s- and p-type ([1s1p]) GTFs are delocalized compared with those determined using the MCMO-HF method. For the H-bonded complexes, differences in the interaction energy induced by the H/D isotope effect were clearly evident because the D...Y bond distance for D complex is longer than the H...Y for H complex. Also, the basis set superposition error for the interaction energy in every H complex was similar to that in every D complex. The results here clearly demonstrate that the protonic and deuteronic basis functions based on alpha(ave) values for correlation effects can be applied to the detailed analysis of the quantum effects of protons and the H/D isotope effect in widespread fields that involve H bonds and weak interactions, such as the function of biological molecules, chemical reaction processes, and the design of new materials.