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. In this article, KEM is extended to provide a full molecule single-determinant N-representable one-body density matrix. A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined. This matrix is converted to a normalized projector by an algorithm due to Clinton. The resulting single-determinant N-representable density matrix maps to a quantum mechanically valid wavefunction which satisfies the variational theorem. The process is demonstrated on clusters of three to twenty water molecules. The resulting energies are more accurate than the straightforward KEM energy results and all violations of the variational theorem are resolved. The N-representability studied in this article is applicable to the study of quantum crystallography. © 2017 Wiley Periodicals, Inc.

Previous research has described the interaction between the novel molecule diethidium (2,7-diamino 9-[2,7 diamino 10-N-phenanthridium] 10-N-phenanthridium) (Figure 1) and B-form DNA. Our goal is the elucidation of diethidium as the first member of a novel class of drugs which are potential pharmaceutical agents. This class of potential drug molecules differs from previously known intercalators in the following ways: a) Its structure, that of two perpendicular planes, each known to have excellent intercalation properties, is novel b) Unlike known bis-intercalators, the linker region length in diethidium is zero c) The geometry of the drug matches the geometry of the space available in the major groove d) The drug is shown to cause some vectorial disruption of DNA. For this paper, we have performed a series of 200 picosecond dynamics simulations on the complex formed between diethidium in the major groove and a dodecarner of double-stranded B-form DNA, CGCGAATTCGCG, and have shown that this complex has a intricate interaction. The DNA dodecamer is found to be in an intermediate A-B state, but, even in simulations as long as 1 nanosecond, the drug does not back-out or otherwise leave the intercalation site. The drug is found to be mobile within the intercalation site on timescales longer than 1 nanoscale. The mobility of the drug within the intercalation site has been predicted by our previous energy minimization studies.

Typical contemporary X‐ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R‐factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.

This research is an effort to further understand the physicochemical interaction between the novel drug molecule diethidium (2,7-diamino 9-[2,7 diamino 10-nN-phenanthridium] 10-nN-phenanthridium) and its biological receptor DNA. The ultimate goal is the elucidation of this novel class of drugs as potential pharmaceutical agents. Understanding the physicochemical properties of this drug as well as the mechanism by which it interacts with DNA should ultimately allow the rational design of novel anti-cancer or anti-viral drugs. A novel binding structure for the diethidium cation to B-form DNA is herein described. Molecular modeling on the complex formed between diethidium and a dodecamer of double-stranded B-form DNA, CGCGAATTCGCG, has shown that this complex is indeed fully capable of participating in the formation of a stable intercalation site. It was expected that diethidium would have a mechanism of intercalation significantly different from other classical intercalators because a) Its structure, that of two perpendicular planes, each known to have excellent intercalation properties, is novel b) The linker region length is zero c) The tilt between the two planes of the drug matches the geometry of the space available to this drug in the major groove. We have studied the complex formed when diethidium enters the central site of the B-DNA dodecamer through the major groove. The complex forms several classes of intercalation structures, which are all stable and vary from "partially intercalated" to "fully intercalated". Multiple minimizations show the drug to be very mobile within the intercalation site. Further, some structures show organization and concomitant stiffening of the DNA above the intercalation site, with a disorganization and disruption of the regular B-DNA structure immediately below the intercalation site. This particular phenomena may be expected to lead to significantly different physicochemical properties for the diethidium complex with respect to other known intercalators, because this sort of vectorial difference in structure above and below the site of intercalation is unknown in existing intercalators, as far as the authors are aware. In addition, we expect the mechanism of interaction between drug and DNA to be described by "direct ligand transfer", wherein the drug is transferred from duplex DNA to duplex DNA without re-entering the solvent. This work is the first instance known to the authors of a novel drug entity that was deduced solely by mathematical reasoning and described subsequently by computational methods. Evidence that diethidium should interact with its target site DNA differently from other known intercalators is strong.