The widely used CHARMM additive all-atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug-like molecules is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chemical groups present in biomolecules and drug-like molecules, including a large number of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concentrating on an extensible force field. Statistics related to the quality of the parametrization with a focus on experimental validation are presented. Additionally, the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3-phenoxymethylpyrrolidine will allow users to readily extend the force field to chemical groups that are not explicitly covered in the force field as well as add functional groups to and link together molecules already available in the force field. CGenFF thus makes it possible to perform "all-CHARMM" simulations on drug-target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems.

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CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields.

A redundant internal coordinate system for optimizing molecular geometries is constructed from all bonds, all valence angles between bonded atoms, and all dihedral angles between bonded atoms. Redundancies are removed by using the generalized inverse of the G matrix; constraints can be added by using an appropriate projector. For minimizations, redundant internal coordinates provide substantial improvements in optimization efficiency over Cartesian and nonredundant internal coordinates, especially for flexible and polycyclic systems. Transition structure searches are also improved when redundant coordinates are used and when the initial steps are guided by the quadratic synchronous transit approach. © 1996 by John Wiley & Sons, Inc.

Using redundant internal coordinates to optimize equilibrium geometries and transition states

Convergence acceleration of iterative sequences. the case of scf iteration

Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.

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Empirical force fields for biological macromolecules: overview and issues.

The capabilities of the Crystal14 program are presented, and the improvements made with respect to the previous Crystal09 version discussed. Crystal14 is an ab initio code that uses a Gaussian-type basis set: both pseudopotential and all-electron strategies are permitted; the latter is not much more expensive than the former up to the first-second transition metal rows of the periodic table. A variety of density functionals is available, including as an extreme case Hartree–Fock; hybrids of various nature (global, range-separated, double) can be used. In particular, a very efficient implementation of global hybrids, such as popular B3LYP and PBE0 prescriptions, allows for such calculations to be performed at relatively low computational cost. The program can treat on the same grounds zero-dimensional (molecules), one-dimensional (polymers), two-dimensional (slabs), as well as three-dimensional (3D; crystals) systems. No spurious 3D periodicity is required for low-dimensional systems as happens when plane-waves are used as a basis set. Symmetry is fully exploited at all steps of the calculation; this permits, for example, to investigate nanotubes of increasing radius at a nearly constant cost (better than linear scaling!) or to perform self-consistent-field (SCF) calculations on fullerenes as large as (10,10), with 6000 atoms, 84,000 atomic orbitals, and 20 SCF cycles, on a single core in one day. Three versions of the code exist, serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated, whereas in the third one the matrices in reciprocal space are distributed for diagonalization. All the relevant vectors are now dynamically allocated and deallocated after use, making Crystal14 much more agile than the previous version, in which they were statically allocated. The program now fits more easily in low-memory machines (as many supercomputers nowadays are). Crystal14 can be used on parallel machines up to a high number of cores (benchmarks up to 10,240 cores are documented) with good scalability, the main limitation remaining the diagonalization step. Many tensorial properties can be evaluated in a fully automated way by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, as well as first and second hyperpolarizabilies, electric field gradients, Born tensors and so forth. Many tools permit a complete analysis of the vibrational properties of crystalline compounds. The infrared and Raman intensities are now computed analytically and related spectra can be generated. Isotopic shifts are easily evaluated, frequencies of only a fragment of a large system computed and nuclear contribution to the dielectric tensor determined. New algorithms have been devised for the investigation of solid solutions and disordered systems. The topological analysis of the electron charge density, according to the Quantum Theory of Atoms in Molecules, is now incorporated in the code via the integrated merge of the Topond package. Electron correlation can be evaluated at the Moller–Plesset second-order level (namely MP2) and a set of double-hybrids are presently available via the integrated merge with the Cryscor program. © 2014 Wiley Periodicals, Inc.

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CRYSTAL14: A program for the ab initio investigation of crystalline solids

Systematic ab initio gradient calculation of molecular geometries, force constants, and dipole moment derivatives is described. A new basis set, denoted 4-21, is presented for first-row atoms. It is nearly equivalent to the 4-31G set but requires less computational effort. Completely optimized Hartree-Fock geometries of 18 molecules are compared using several basis sets, with and without polarization functions. The question of the best representation of molecular force fields is discussed, and a set of standardized internal coordinates is suggested for future work. Quadratic and the most important cubic force constants and dipole moment derivatives of first-row hydrides are calculated using the 4-21 basis set, and the results are compared with those from other basis sets, including near-Hartree-Fock ones. Force-field calculations on larger molecules with the 4-21 basis are summarized. A general formulation of the rotational correction to dipole moment derivatives is given.

Systematic AB Initio Gradient Calculation of Molecular Geometries, Force Constants, and Dipole Moment Derivatives

The molecular structure of toluene

The structures of fluorobenzene, 1,3-difluorobenzene, 1,3,5-trifluorobenzene, 1,2,3-trifluorobenzene, pentafluorobenzene, and hexafluorobenzene have been determined by the ab initio gradient method with a 4-21 basis set. Approximate corrections have been developed to yield re and r0 structures so that comparison can be made with the available experimental information. The CF bond distance decreases in a uniform manner with increasing fluorination of the ring, either on adjacent or on meta sites. The ring structure also shows systematic deformation, with a decrease of about 0.01 A in the CC bond length adjacent to the point of substitution and an increase of about 2.5˚ in the ring angle at the substitution site in those cases where the requirement of ring closure permits.

Structures of some fluorinated benzenes determined by ab initio computation

The structures of pyridine, pyrimidine, pyrazine, and s-triazine have been determined by the ab initio gradient method with a 4–21 basis set augmented by addition of polarization functions on the nitrogen atoms. The effect of omission of the polarization functions is also investigated. Corrections have been applied to yield computed r 0 structures, assuming approximate constancy of the effects of neglect of electron correlation, use of a finite basis set, and correction for zero-point vibrations. The validity of these assumptions is carefully evaluated, and the results are shown to agree with the best available experimental evidence to a high degree of accuracy. The effect of nitrogen atoms on the ring structure is quite systematic, with a sharp decrease in the ring angles at nitrogen, becoming progressively greater as more nitrogen atoms are substituted for carbon. There is little change in CN distances between the compounds.

Frank Pang

Papers

Systematic AB Initio Gradient Calculation of Molecular Geometries, Force Constants, and Dipole Moment Derivatives

The molecular structure of toluene

Structures of some fluorinated benzenes determined by ab initio computation

The structure of some nitrogen heteroaromatics

The structural effects of fluorine substitution in pyridine, pyrimidine, and s‐triazine: An ab initio study