Quantum Crystallography: Current Developments and Future Perspectives.

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated.

Quantum crystallography: A perspective.

Extraction of the complete quantum mechanics from X-ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X-ray diffraction data into an electron density that reflects the antisymmetry of an N-electron wave function.

Notes on The Energy Equivalence of Information.

Maxwell's demon makes observations and thereby collects information. As Brillouin points out such information is the negative of entropy (negentropy) and is the equivalent of a cost in energy. The energy cost of information can be quantified in the relationship E = kT ln 2, where k is the Boltzmann constant, T is the absolute temperature, and the factor ln 2 arises from the existence of two possibilities for a "yes/no" circumstance, as, for example, in the passage of a proton through a barrier controlled by a Maxwell's demon.

Single determinant N-representability and the kernel energy method applied to water clusters.

The Kernel energy method (KEM) is a quantum chemical calculation method that has been shown to provide accurate energies for large molecules. KEM performs calculations on subsets of a molecule (called kernels) and so the computational difficulty of KEM calculations scales more softly than full molecule methods. Although KEM provides accurate energies those energies are not required to satisfy the variational theorem.

Energy Equivalence of Information in the Mitochondrion and the Thermodynamic Efficiency of ATP Synthase.

Half a century ago, Johnson and Knudsen resolved the puzzle of the apparent low efficiency of the kidney (∼ 0.5%) compared to most other bodily organs (∼ 40%) by taking into account the entropic cost of ion sorting, the principal function of this organ. Similarly, it is shown that the efficiency of energy transduction of the chemiosmotic proton-motive force by ATP synthase is closer to 90% instead of the oft-quoted textbook value of only 60% when information theoretic considerations are applied to the mitochondrion.

The localization-delocalization matrix and the electron-density-weighted connectivity matrix of a finite graphene nanoribbon reconstructed from kernel fragments.

Bader's quantum theory of atoms in molecules (QTAIM) and chemical graph theory, merged in the localization-delocalization matrices (LDMs) and the electron-density-weighted connectivity matrices (EDWCM), are shown to benefit in computational speed from the kernel energy method (KEM). The LDM and EDWCM quantum chemical graph matrices of a 66-atom C46H20 hydrogen-terminated armchair graphene nanoribbon, in 14 (2×7) rings of C2v symmetry, are accurately reconstructed from kernel fragments. (This includes the full sets of electron densities at 84 bond critical points and 19 ring critical points, and the full sets of 66 localization and 4290 delocalization indices (LIs and DIs).

Wigner high-electron-correlation regime of nonuniform density systems: A quantal-density-functional-theory study.

The Wigner regime of a system of electrons in an external field is characterized by a low electron density and a high electron-interaction energy relative to the kinetic energy. The low correlation regime is in turn described by a high electron density and an electron-interaction energy smaller than the kinetic energy. The Wigner regime of a nonuniform electron density system is investigated via quantal density functional theory (QDFT).

Wigner High Electron Correlation Regime in Nonuniform Electron Density Systems: Kinetic and Correlation-Kinetic Aspects.

The Wigner high electron correlation regime is characterized in the literature by an electron-interaction energy much greater than the kinetic energy. Via the 'quantal Newtonian' first law, we discover that for a nonuniform electron density system in this regime, there is a 'quantal compression' of the kinetic energy density. The explanation of this compression provides a fundamental understanding for why the kinetic energy is a smaller fraction of the total energy relative to the same ratio in the low correlation regime.

Protoribosome by quantum kernel energy method.

Experimental evidence suggests the existence of an RNA molecular prebiotic entity, called by us the "protoribosome," which may have evolved in the RNA world before evolution of the genetic code and proteins. This vestige of the RNA world, which possesses all of the capabilities required for peptide bond formation, seems to be still functioning in the heart of all of the contemporary ribosome. Within the modern ribosome this remnant includes the peptidyl transferase center.

Ground-state features in the THz spectra of molecular clusters of β-HMX.

We present calculations of absorption spectra arising from molecular vibrations at THz frequencies for molecular clusters of the explosive HMX using density functional theory (DFT). The features of these spectra can be shown to follow from the coupling of vibrational modes. In particular, the coupling among ground-state vibrational modes provides a reasonable molecular-level interpretation of spectral features associated with the vibrational modes of molecular clusters.

Quantum kernel applications in medicinal chemistry.

Progress in the quantum mechanics of biological molecules is being driven by computational advances. The notion of quantum kernels can be introduced to simplify the formalism of quantum mechanics, making it especially suitable for parallel computation of very large biological molecules. The essential idea is to mathematically break large biological molecules into smaller kernels that are calculationally tractable, and then to represent the full molecule by a summation over the kernels.

New structures of hydronium cation clusters.

Four new hydronium ion structures are investigated by means of quantum mechanical calculations at the DFT/B3LYP6-311+G(2d,2p) level of theory. There exist experimental crystallographic hydronium cations (HO ) of two different geometrical structures, one BEXFEQ (acyclic) and one IYEPEH (cyclic). Molecular calculations reveal their relative stability.

6-bromoindigo dye.

6-Bromoindigo (MBI) [systematic name: 6-bromo-2-(3-oxo-2,3-dihydro-1H-indol-2-ylidene)-2,3-dihydro-1H-indol-3-one], C(16)H(9)BrN(2)O(2), crystallizes with one disordered molecule in the asymmetric unit about a pseudo-inversion center, as shown by the Br-atom disorder of 0.682 (3):0.318 (3).

Ion induced dipole clusters H(n)- (3 ≤ n-odd ≤ 13): density functional theory calculations of structure and energy.

We investigate anew the possible equilibrium geometries of ion induced dipole clusters of hydrogen molecular ions, of molecular formula H(n)(-) (3 ≤ n-odd ≤ 13). Our previous publications [Sapse, A. M.

Characterization of a trihydrogen bond on the basis of the topology of the electron density.

Recent DFT calculations have predicted unexpected molecular structures for the ion induced dipole clusters H(n)(-) (3 ≤ n-odd ≤ 13). Analysis of these calculations suggests the definition of a new bond, called the trihydogen bond (THB). This is placed in context by a review and classification of multihydrogen interactions as usually discussed in the literature.

The Kernel Energy Method: Construction of 3 & 4 tuple Kernels from a List of Double Kernel Interactions.

The Kernel Energy Method (KEM) provides a way to calculate the ab-initio energy of very large biological molecules. The results are accurate, and the computational time reduced. However, by use of a list of double kernel interactions a significant additional reduction of computational effort may be achieved, still retaining ab-initio accuracy.

A generalized higher order kernel energy approximation method.

We present a general mathematical model that can be used to improve almost all fragment-based methods for ab initio calculation of total molecular energy. Fragment-based methods of computing total molecular energy mathematically decompose a molecule into smaller fragments, quantum-mechanically compute the energies of single and multiple fragments, and then combine the computed fragment energies in some particular way to compute the total molecular energy. Because the kernel energy method (KEM) is a fragment-based method that has been used with much success on many biological molecules, our model is presented in the context of the KEM in particular.

Calculation of strong and weak interactions in TDA1 and RangDP52 by the kernel energy method.

Using the Kernel Energy Method we apply ab initio quantum mechanics to study the relative importance of weak and strong interactions (including hydrogen bonds) in the crystal structures of the title compounds TDA1 and RangDP52. Perhaps contrary to widespread belief, in these compounds the weak interaction energies, because of their large number and cooperativity, can be significant to the binding energetics of the crystal, and thus also to its other properties.

Kernel energy method applied to vesicular stomatitis virus nucleoprotein.

The kernel energy method (KEM) is applied to the vesicular stomatitis virus (VSV) nucleoprotein (PDB ID code 2QVJ). The calculations employ atomic coordinates from the crystal structure at 2.8-A resolution, except for the hydrogen atoms, whose positions were modeled by using the computer program HYPERCHEM.

Calculated interactions of a nitro group with aromatic rings of crystalline picryl bromide.

Several crystalline polymorphs have been discovered for picryl bromide. Among the several forces that control the formation of such polymorphs are the interactions among the nitro groups and phenyl rings of those crystals. Although there are >300 structures to be found in the Cambridge Structural Database displaying the nitro-phenyl interaction, nonetheless this interesting, and apparently important, interaction, seems not to have been discussed within any of the papers reporting the structures.

The kernel energy method of quantum mechanical approximation carried to fourth-order terms.

It is now possible to calculate the ab initio quantum mechanics of very large biological molecules. Two things lead to this perspective, namely, (i) the advances of parallel supercomputers, and (ii) the discovery of a quantum formalism called quantum crystallography and the use of quantum kernels, a method that is well suited for parallel computation. The kernel energy method (KEM) carried to second order has been used to calculate the quantum mechanical ab initio molecular energy of peptides, protein (insulin and collagen), DNA, and RNA and the interaction of drugs with their biochemical molecular targets.