This article attempts to bring together basic and complex information which has been gathered on cellulose structure, principally that of native cellulose, over the last few decades. Even though advances have been made in the field of crystallography, powder crystallography cannot yield a definitive cellulose structure and single crystal diffraction is not possible due to the lack of suitable crystals. Knowledge obtained on the biosynthesis of native cellulose and on the polymorphy of cellulose and its derivatives help our understanding of ultrastructure. Many inconsistencies between early crystallographic studies of native cellulose have been clarified by the discovery that two polymorphs (α and β) of cellulose I exist. Models of the possible ultrastructural arrangements within native cellulose have been put forward over the decades; with advancement in technology, computer simulations of small and large systems are being created to test the viability of these ultrastructural models. It is hoped that this review will aid in the understanding of the complexity and uncertainties that still exist in this subject

Cellulose: the structure slowly unravels

A hierarchy of three models for combined quantum mechanical (QM) and molecular mechanical (MM) approaches is presented. They simplify the QM description of large molecules by reducing it to the electronically important fragment which interacts with the molecular mechanically treated remainder of the molecule. In the simplest model A, the QM fragments are only mechanically embedded in their MM environment. The more refined models B and C include a quantum mechanical treatment of electrostatic interactions between the fragments and a semiclassical description of polarization. The implementation of models A-C for MNDO type wavefunctions and the MM3 force field is outlined. Selected applications in organic chemistry are discussed, addressing the ability of the proposed models to reproduce substituent effects (MM) on chemical structure and reactivity (QM). These applications include protonations, deprotonations, hydride transfer reactions, nucleophilic additions, and nucleophilic ring cleavage reactions.

Hybrid Models for Combined Quantum Mechanical and Molecular Mechanical Approaches

The Tinker software, currently released as version 8, is a modular molecular mechanics and dynamics package written primarily in a standard, easily portable dialect of Fortran 95 with OpenMP extensions It supports a wide variety of force fields, including polarizable models such as the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field The package runs on Linux, macOS, and Windows systems In addition to canonical Tinker, there are branches, Tinker-HP and Tinker-OpenMM, designed for use on message passing interface (MPI) parallel distributed memory supercomputers and state-of-the-art graphical processing units (GPUs), respectively The Tinker suite also includes a tightly integrated Java-based graphical user interface called Force Field Explorer (FFE), which provides molecular visualization capabilities as well as the ability to launch and control Tinker calculations

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Tinker 8: Software Tools for Molecular Design.

This article describes the parameterization and performance of MMFF94 for molecular geometries and deformations. It defines the form used for the valence-coordinate terms that represent variations in bond lengths and angles, and it describes the derivation of quadratic force constants from HF/6-31G* data and the derivation of reference bond lengths and angles from fits to MP2/6-31G*-optimized geometries. Comparisons offered show that MMFF94 accurately reproduces the computational data used in its parameterization and demonstrate that its derivation from such data simultaneously confers the ability to reproduce experiment. In particular, MMFF94 reproduces experimentally determined bond lengths and angles for 30 organic molecules with root mean square (rms) deviations of 0.014 A and 1.2°, respectively. MM3 reproduces bond angles to the same accuracy, but reproduces experimental bond lengths more accurately, in part because it was fit directly to thermally averaged experimental bond lengths; MMFF94, in contrast, was fit to (usually shorter) energy-minimum values, as is proper for an anharmonic force field intended for use in molecular-dynamics simulations. The comparisons also show that UFF and a recent version of CHARMm (QUANTA 3.3 parameterization) are less accurate for molecular geometries than either MMFF94 or MM3. For vibrational frequencies, MMFF94 and MM3 give comparable overall rms deviations versus experiment of 61 cm−1 and 57 cm−1, respectively, for 15 small, mostly organic molecules. In a number of instances, MM3's derivation employed observed frequencies that differ substantially—by nearly 400 cm−1 in one case—from other published frequencies which had themselves been confirmed theoretically by good-quality ab initio calculations. Overall, the comparisons to experimental geometries and vibrational frequencies demonstrate that MMFF94 achieves MM3-like accuracy for organic systems for which MM3 has been parameterized. Because MMFF94 is derived mainly from computational data, however, it has been possible to parameterize MMFF94 with equal rigor for a wide variety of additional systems for which little or no useful experimental data exist. Equally good performance can be expected for such systems. © John Wiley & Sons, Inc.

Merck Molecular Force Field. III. Molecular Geometries and Vibrational Frequencies for MMFF94

A recent extension of the polarizable continuum solvation model (PCM) to excited electronic states is applied to the study of solvent effects on electronic transitions, accounting for both electrostatic and nonelectrostatic solute–solvent interactions. A general formalism for nonequilibrium electrostatic solvation is developed, applicable to all PCM versions, and a recent procedure for the quantum-mechanical computation of dispersion and repulsion solute–solvent interactions is implemented and used for the first time in this context. The procedure is applied to the study of the n→π* transition of acetone in aqueous and nonaqueous solvents: nonequilibrium effects are very important in polar environments; also, the inclusion of dispersion and repulsion is mandatory to obtain the correct trend of the solvatochromic shifts. The effect of adding some explicit solvent molecules is also analyzed.

Solvent effect on vertical electronic transitions by the polarizable continuum model

The molecular mechanics (MMP2) program and procedures for the treatment of conjugated hydrocarbons, and some of the results which they can achieve are described. The program is an updated version of the similar MMP1 program, but contains some differences. It is based on an SCF π system calculation, rather than on the VESCF method used earlier. All parameters are compatible with those in the MM2 program. Hence it is possible to calculate heats of formation, resonance energies, and structures for conjugated hydrocarbons in a way that is consistent with the calculations on non-conjugated molecules. The overall results as far as structure and energy are somewhat better than they were with the MMP1 program.

The MMP2 calculational method

The MM3 force field has been extended to cover aromatic heterocycles of the pyridine and pyrrole types. Structures (32 compounds), heats of formation (35 compounds), dipole moments (35 compounds), and vibrational spectra (11 compounds) have been examined, and the results are good for structure and fair for the other its

Molecular mechanics (MM3). Calculations on nitrogen-containing aromatic heterocycles

The MMZ program has been extended so as to be able to deal with conjugated nitrogen containing molecules (MMZ(~S) ) . The simple heterocycles, pyridine and pyrrole and several other molecules with pyridine-type and pyrrole-type nitrogen atoms, were examined and used to parameterize MM2. Calculations were then camed out with about 25 additional and more complicated heterocycles, and the calculated structures are compared with the experimental ones. The agreement is generally good, but problems remain. The source of these problems and their possible future corrections are discussed. The heats of formation were calculated for 11 compounds containing pyridine-type nitrogen atoms. The agreement with the experimental values is

Julia C. Tai

Papers

The MMP2 calculational method

Molecular mechanics (MM3). Calculations on nitrogen-containing aromatic heterocycles

Molecular mechanics calculations on conjugated nitrogen-containing heterocycles

Conformational analysis. 120. Small polyenes

Organic quantum chemistry. XIX. Calculation of the electronic spectra of unsaturated ketones