ABSTRACT:We describe a kernel energy method (KEM) for applying quantum crystallography to large molecules, with an emphasis on the calculation of the molecular energy of peptides. The computational difficulty of representing the system increases only modestly with the number of atoms. The calculations are carried out on modern parallel supercomputers. By adopting the approximation that a full biological molecule can be represented by smaller "kernels" of atoms, the calculations are greatly simplified. Moreover, collections of kernels are, from a computational point of view, well suited for parallel computation. The result is a modest increase in computational time as the number of atoms increases, while retaining the ab initio character of the calculations. We describe a test of our method, and establish its accuracy using 15 different peptides of biological interest.

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. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

We have investigated the heretofore unknown unimolecular decomposition pathway of the explosive molecule diaminodinitroethylene (DADNE). With the use of DFT methods, whose accuracy has been calibrated by means of ab initio calculations (MP2, MP4, G2) on a simpler but related molecule, nitroethylene, we have been able to characterize the entire decomposition reaction pathway. Importantly, we find that the reaction is initiated by a nitro-to-nitrite rearrangement with a calculated energy barrier of magnitude 59.1 kcal/mol obtained by use of B3LYP (59.7 kcal/mol B3P86) which is very close to the experimental activation energy of 58 kcal/mol. We have been able to characterize every step in the decomposition reaction path leading to fragments NO, HONO, CO, NH2, and HNC. These may interact to yield final stable products, CO, N2, H2O with an energy release that on average is adequate to initiate two additional DADNE molecular decompositions, and thus, sustain a chain reaction. The structural parameters we have calculated for DADNE are consistent with the known experimental crystallographic structure, and also with previous theoretical calculations. Additionally, we have obtained the structural parameters of the initial transition state, as well as each subsequent step along the decomposition pathway. Thus we consider the unimolecular decomposition of DADNE to be well characterized.

Using quantum mechanics and exploiting known crystallographic coordinates of tRNA substrate located in the ribosome peptidyl transferase center around the 2-fold axis, we have investigated the mechanism for peptide-bond formation. The calculation is based on a choice of 50 atoms assumed to be important in the mechanism. We used density functional theory to optimize the geometry and energy of the transition state (TS) for peptide-bond formation. The TS is formed simultaneously with the rotatory motion enabling the translocation of the A-site tRNA 3′ end into the P site, and we estimated the magnitude of rotation angle between the A-site starting position and the place at which the TS occurs. The calculated TS activation energy, E a , is 35.5 kcal (1 kcal = 4.18 kJ)/mol, and the increase in hydrogen bonding between the rotating A-site tRNA and ribosome nucleotides as the TS forms appears to stabilize it to a value qualitatively estimated to be ≈18 kcal/mol. The optimized geometry corresponds to a structure in which the peptide bond is being formed as other bonds are being broken, in such a manner as to release the P-site tRNA so that it may exit as a free molecule and be replaced by the translocating A-site tRNA. At TS formation the 2′ OH group of the P-site tRNA A76 forms a hydrogen bond with the oxygen atom of the carboxyl group of the amino acid attached to the A-site tRNA, which may be indicative of its catalytic role, consistent with recent biochemical experiments.

In the search for boron nanotubes, the geometrical duals of carbon nanotubes, we employ the Euler−Poincare formula for a cylinder, P − C + F = 0. As may be seen in the attached figure, boron nanotubes may be imagined as arising from a correspondence between a boron atom and the center of each of the faces in a carbon nanotube.

We explain by quantal density functional theory the physics of mapping from any bound nondegenerate excited state of Schrödinger theory to an S system of noninteracting fermions with equivalent density and energy. The S system may be in a ground or excited state. In either case, the highest occupied eigenvalue is the negative of the ionization potential. We demonstrate this physics with examples. The theory further provides a new framework for calculations of atomic excited states including multiplet structure.

The kernel energy method (KEM) has been used in three recent papers (1-3) to calculate the quantum mechanical ab inito molecular energy of peptides and the protein insulin. It was found to have good accuracy. The computational difficulty of representing a molecule increases only modestly with the number of atoms. The calculations are simplified by adopting the approximation that a full biological molecule can be represented by smaller "kernels" of atoms. In this paper, the accuracy of the KEM is tested in the application to DNA, whose basic kernels, chemical bonding, and overall molecular structure are quite different from peptides and proteins. The basic kernel in the case of peptides and proteins is an amino acid. The basic kernel in the case of DNA is a nucleotide consisting of a phosphate-sugar-base. The molecular energy is calculated for all three basic types of DNA, i.e., B, A, and Z configurations of DNA. The results give an accuracy that is comparable to that achieved with peptides and proteins. Thus, the KEM is found to be applicable to major types of biological molecules.

Four distinct pathways of unimolecular decomposition of nitroethylene, the C−NO2 bond breaking, nitro-to-nitrite rearrangement, 1,2-elimination reaction and 1,1-elimination reaction, have been computationally investigated with ab initio, MP2, MP4, and G2 methods as well as with DFT methods. The nitro-to-nitrite rearrangement and 1,2-elimination reaction are found to give the lowest energy decomposition pathways for this molecule, about 15 kcal/mol lower than the cleavage of the nitro group.