Variational and perturbative formulations of QM/MM free energy with mean-field embedding and its analytical gradients

Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent with the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an SN2 Menshutkin reaction in water, NH3 + CH3CL -> NH3CH3^{+} + CL^{-}, for which free energy profiles are obtained at the HF, MP2, B3LYP, and BH&HLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be < 0.5 kcal/mol using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water.Comment: 17 pages, 8 figures. J.Chem.Phys. 129, 244104 (2008

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

A survey of the ESR model for an objective reinterpretation of quantum mechanics

Most scholars concerned with the foundations of quantum mechanics (QM) think that contextuality and nonlocality (hence nonobjectivity of physical properties) are unavoidable features of QM which follow from the mathematical apparatus of QM. Moreover these features are usually considered as basic in quantum information processing. Nevertheless they raise still unsolved problems, as the objectification problem in the quantum theory of measurement. The extended semantic realism (ESR) model offers a possible way out from these difficulties by embedding the mathematical formalism of QM into a broader mathematical formalism and reinterpreting quantum probabilities as conditional on detection rather than absolute. The embedding allows to recover the formal apparatus of QM within the ESR model, and the reinterpretation of QM allows to construct a noncontextual hidden variables theory which justifies the assumptions introduced in the ESR model and proves its objectivity. According to the ESR model both linear and nonlinear time evolution occur, depending on the physical environment, as in QM. In addition, the ESR model, though objective, implies modified Bell's inequalities that do not conflict with QM, supplies different mathematical representations of proper and improper mixtures, provides a general framework in which the local interpretations of the GHZ experiment obtained by other authors are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth.Comment: 12 page