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Register a new userQuantum Mechanics / Coarse-Grained Molecular Mechanics (QM/CG-MM)
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Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the slow sampling of the large configuration space for the MM part, the high cost of repetitive QM computations for changing coordinates of atoms in the MM surroundings, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of bottom-up coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantum mechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.
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We study the interaction between two neutral atoms or molecules subject to a uniform static electric field, using quantum mechanics (QM) and quantum electrodynamics (QED) applied to coupled harmonic Drude oscillators. Our focus is to understand the interplay between dispersion interactions and field-induced electrostatics and polarization in both retarded and non-retarded regimes. We present an exact solution for two coupled oscillators using QM and Rayleigh-Schrodinger perturbation theory, demonstrating that the external field controls the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by QED and rationalized by stochastic electrodynamics, our analysis shows that field-induced electrostatics and polarization terms remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded QM description, in contrast to a recent work. Our framework combining four complementary theoretical approaches paves the way to a systematic description and enhanced understanding of molecular interactions under the combined action of external and vacuum fields.
A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on the basis of virtual plane waves.
A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane waves. The ground state energy of a hydrogen atom is calculated in a special way, regarding explicitly all the terms of electrostatic and kinetic energies. The correct values of the ground state energy and the radius of decay are achieved only when the electrostatic energies of the electron and the proton (self-energies) are not taken into account. This proves again that self-action should be excluded in quantum mechanics. A model of a spherical ball with uniformly distributed charge of particles is considered. It is shown that for a neutral ball (with compensated electric charge) the electrostatic energy is a non-zero negative value in this model. This occurs because the self-energy of the constituting particles should be subtracted. So it shown that the energy of the electric field does not have to be of a positive value in any imaginable problem.
QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We prove the reliability of the error indicator (upper bound of the true approximation error) and develop some sampling techniques for its efficient calculation. Based on the error indicator and D{o}rfler marking strategy, we design an adaptive QM/MM algorithm for crystalline defects and demonstrate the efficiency with some numerical experiments.
Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Trade-offs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multi-scale QM/MM or iterative approach. Limitations to both conventional density functional theory (DFT) and classical MM force fields remain for describing non-covalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e., electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.
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