General Force Field Research Articles

Optimized Lennard-Jones Parameters for Druglike Small Molecules.

Meaningful efforts in computer-aided drug design (CADD) require accurate molecular mechanical force fields to quantitatively characterize protein-ligand interactions, ligand hydration free energies, and other ligand physical properties. Atomic models of new compounds are commonly generated by analogy from the predefined tabulated parameters of a given force field. Two widely used approaches following this strategy are the General Amber Force Field (GAFF) and the CHARMM General Force Field (CGenFF). An important limitation of using pretabulated parameter values is that they may be inadequate in the context of a specific molecule. To resolve this issue, we previously introduced the General Automated Atomic Model Parameterization (GAAMP) for automatically generating the parameters of atomic models of small molecules, using the results from ab initio quantum mechanical (QM) calculations as target data. The GAAMP protocol uses QM data to optimize the bond, valence angle, and dihedral angle internal parameters, and atomic partial charges. However, since the treatment of van der Waals interactions based on QM is challenging and may often be unreliable, the Lennard-Jones 6-12 parameters are kept unchanged from the initial atom types assignments (GAFF or CGenFF), which limits the accuracy that can be achieved by these models. To address this issue, a new set of Lennard-Jones 6-12 parameters was systematically optimized to reproduce experimental neat liquid densities and enthalpies of vaporization for a large set of 430 compounds, covering a wide range of chemical functionalities. Calculations of the hydration free energy indicate that optimal accuracy for these models is achieved when the molecule-water van der Waals dispersion is rescaled by a factor of 1.115. The final optimized model yields an average unsigned error of 0.79 kcal/mol in the hydration free energies.

Polarizable Force Field for Molecular Ions Based on the Classical Drude Oscillator.

Development of accurate force field parameters for molecular ions in the context of a polarizable energy function based on the classical Drude oscillator is a crucial step toward an accurate polarizable model for modeling and simulations of biological macromolecules. Toward this goal we have undertaken a hierarchical approach in which force field parameter optimization is initially performed for small molecules for which experimental data exists that serve as building blocks of macromolecular systems. Small molecules representative of the ionic moieties of biological macromolecules include the cationic ammonium and methyl substituted ammonium derivatives, imidazolium, guanidinium and methylguanidinium, and the anionic acetate, phenolate, and alkanethiolates. In the present work, parameters for molecular ions in the context of the Drude polarizable force field are optimized and compared to results from the nonpolarizable additive CHARMM general force field (CGenFF). Electrostatic and Lennard-Jones parameters for the model compounds are developed in the context of the polarizable SWM4-NDP water model, with emphasis on assuring that the hydration free energies are consistent with previously reported parameters for atomic ions. The final parameters are shown to be in good agreement with the selected quantum mechanical (QM) and experimental target data. Analysis of the structure of water around the ions reveals substantial differences between the Drude and additive force fields indicating the important role of polarization in dictating the molecular details of aqueous solvation. The presented parameters represent the foundation for the charged functionalities in future generations of the Drude polarizable force field for biological macromolecules as well as for drug-like molecules.

Diffusion of Trimethylbenzenes, Toluene, and Xylenes in UWY Zeolite as a Catalyst for Transalkylation of Trimethylbenzenes with Toluene

A molecular dynamics study has been carried out on the diffusion of trimethylbenzene (TMB), toluene, and xylene molecules in transalkylation of TMB and toluene in UWY zeolite, containing crossing 10-ring and 12-ring channels. Two models of UWY have been employed, the pure silica and an acidic form of UWY including Al and Bronsted sites, using a recently parameterized general force field for zeotypes, which reproduce pore diameters within ca. ±0.2 A. Molecular traffic has been observed from the result of TMBs using almost exclusively the 12-ring channels and the preferential location of p-xylene and toluene in the 10-ring channels at high loading (reaction conditions). From the three different 10-ring channels, only p-xylene and toluene can fit in the two smallest channels, whereas m-xylene and 1,2,4-TMB can also diffuse in the largest 10-ring channel. An in-depth analysis of transition-state shape selectivity has been performed, showing that all transition states of transalkylation of toluene and TMBs can...

Evaluation of General and Tailor Made Force Fields via X-ray Thermal Diffuse Scattering Using Molecular Dynamics and Monte Carlo Simulations of Crystalline Aspirin.

We have performed a comparison of the experimental thermal diffuse scattering (TDS) from crystalline Aspirin (form I) to that calculated from molecular dynamics (MD) simulations based on a variety of general force fields and a tailor-made force field (TMFF). A comparison is also made with Monte Carlo (MC) simulations which use a "harmonic network" approach to describe the intermolecular interactions. These comparisons were based on the hypothesis that TDS could be a useful experimental data in validation of such simulation parameter sets, especially when calculations of dynamical properties (e.g., thermodynamic free energies) from molecular crystals are concerned. Currently such a validation of force field parameters against experimental data is often limited to calculation of specific physical properties, e.g., absolute lattice energies usually at 0 K or heat capacity measurements. TDS harvested from in-house or synchrotron experiments comprises highly detailed structural information representative of the dynamical motions of the crystal lattice. Thus, TDS is a well-suited experimental data-driven means of cross validating theoretical approaches targeted at understanding dynamical properties of crystals. We found from the results of our investigation that the TMFF and COMPASS (from the commercial software "Materials Studio") parameter sets gave the best agreement with experiment. From our homologous MC simulation analysis we are able to show that force constants associated with the molecular torsion angles are likely to be a strong contributing factor for the apparent reason why these aforementioned force fields performed better.

Improved Accuracy and Convergence of Intrinsically Disordered Protein Molecular Dynamics Simulations Using the ff14IDPSFF Force Field

Vital components in signaling pathways, regulation, and other complex biochemical networks, intrinsically disordered proteins (IDPs) utilize their conformational flexibility to perform intricate functions, but their flexible conformations remain poorly understood. A mounting body of experimental evidence – ranging from NMR structural studies to X-ray crystallography experiments – has accumulated to probe the conformations of IDPs. However, IDPs remain elusive by standard experimental methods due to their conformational flexibility. Molecular dynamics (MD) simulations can provide detailed insight into these complex structure-function dynamics if they can reproduce available experimental observables. The recently developed ff14IDPSFF force field developed by Song et. al [2017] corrects dihedral backbone terms of all 20 canonical amino acids to achieve this goal. Utilizing this recently-developed force field, 9 unstructured short peptides and the HIVrev IDP were simulated extensively to assess the quality of the new force field and to assess the computational challenge of IDP simulations in general. We extended trajectory lengths for at least one microsecond and to at least ten independent trajectories to comprehensively evaluate the performance, accuracy, and convergence of MD simulations in f14IDPSF. All simulated f14IDPSFF values (Cα chemical shift, J-coupling, RDC) are in close agreement to available NMR-derived experimental values than the generic protein force field ff14SB. Simulated ff14IDPSFF values also converged within nanosecond timescales for the 9 short peptides whereas simulated ff14SB values converged after 1 μs. HIVrev simulated values converged after 1 μs for both ff14IDPSFF and ff14SB, which are expected due to its larger size. Improved accuracy to experimental values and timescale of calculation convergence demonstrate the utility of ff14IDPSFF to explore IDP conformation space and investigate the structure-function dynamics of IDPs.

Effects of Force Field Selection on the Computational Ranking of MOFs for CO2 Separations.

Metal–organic frameworks (MOFs) have been considered as highly promising materials for adsorption-based CO2 separations. The number of synthesized MOFs has been increasing very rapidly. High-throughput molecular simulations are very useful to screen large numbers of MOFs in order to identify the most promising adsorbents prior to extensive experimental studies. Results of molecular simulations depend on the force field used to define the interactions between gas molecules and MOFs. Choosing the appropriate force field for MOFs is essential to make reliable predictions about the materials’ performance. In this work, we performed two sets of molecular simulations using the two widely used generic force fields, Dreiding and UFF, and obtained adsorption data of CO2/H2, CO2/N2, and CO2/CH4 mixtures in 100 different MOF structures. Using this adsorption data, several adsorbent evaluation metrics including selectivity, working capacity, sorbent selection parameter, and percent regenerability were computed for each MOF. MOFs were then ranked based on these evaluation metrics, and top performing materials were identified. We then examined the sensitivity of the MOF rankings to the force field type. Our results showed that although there are significant quantitative differences between some adsorbent evaluation metrics computed using different force fields, rankings of the top MOF adsorbents for CO2 separations are generally similar: 8, 8, and 9 out of the top 10 most selective MOFs were found to be identical in the ranking for CO2/H2, CO2/N2, and CO2/CH4 separations using Dreiding and UFF. We finally suggested a force field factor depending on the energy parameters of atoms present in the MOFs to quantify the robustness of the simulation results to the force field selection. This easily computable factor will be highly useful to determine whether the results are sensitive to the force field type or not prior to performing computationally demanding molecular simulations.

Potential of polarizable force fields for predicting the separation performance of small hydrocarbons in M-MOF-74.

The separation of light olefins from paraffins via cryogenic distillation is a very energy intensive process. Solid adsorbents and especially metal-organic frameworks with open metal sites have the potential to significantly lower the required energy. Specifically, M-MOF-74 has drawn considerable attention for application in olefin/paraffin separation. To investigate how the separation proceeds on a molecular level and to design better materials, molecular simulation can be a useful tool. Unfortunately, it is still a challenge to model the adsorption behavior of many adsorbates in metal-organic frameworks with open metal sites. Previously, the inclusion of explicit polarization has been suggested to improve the quality of classical force fields for such systems. Here, the potential of polarizable force fields for the description of olefins and paraffins in metal-organic frameworks with open metal sites is investigated. In particular, heats of adsorption, binding geometries, and adsorption isotherms are calculated for C2H4, C2H6, C3H6, and C3H8 in M-MOF-74 (with M = Co, Mn, Fe, and Ni). In this study, no force field parameters are adjusted to improve the model. The results show that including explicit polarization significantly improves the description of the adsorption in comparison to non-polarizable generic force fields which do not consider explicit polarization. The study also reveals that simulation predictions are sensitive to the assigned repulsive potential and framework charges. A fully re-parametrized polarizable force field may have the capability to improve the predictions even further.

Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields

In this paper, the brachistochronic motion of a mechanical system composed of variable-mass particles is analysed. Workless (ideal) holonomic and linear nonholonomic constraints are imposed on the system. It is assumed that the system moves in an arbitrary field of known potential and nonpotential forces with prescribed both laws of the time-rate of mass variation of the particles and relative velocities of the expelled (or gained) masses. The first time-derivatives of quasi-velocities are taken as control variables. Using Pontryagin’s maximum principle and singular optimal control theory, the problem of brachistochronic motion of the nonholonomic variable-mass mechanical system is solved as a two-point boundary value problem. In addition, a discussion about the realization of control forces is given. The results are illustrated via an example.

A general intermolecular force field based on tight-binding quantum chemical calculations.

A black-box type procedure is presented for the generation of a molecule-specific, intermolecular potential energy function. The method uses quantum chemical (QC) information from our recently published extended tight-binding semi-empirical scheme (GFN-xTB) and can treat non-covalently bound complexes and aggregates with almost arbitrary chemical structure. The necessary QC information consists of the equilibrium structure, Mulliken atomic charges, charge centers of localized molecular orbitals, and also of frontier orbitals and orbital energies. The molecular pair potential includes model density dependent Pauli repulsion, penetration, as well as point charge electrostatics, the newly developed D4 dispersion energy model, Drude oscillators for polarization, and a charge-transfer term. Only one element-specific and about 20 global empirical parameters are needed to cover systems with nuclear charges up to radon (Z = 86). The method is tested for standard small molecule interaction energy benchmark sets where it provides accurate intermolecular energies and equilibrium distances. Examples for structures with a few hundred atoms including charged systems demonstrate the versatility of the approach. The method is implemented in a stand-alone computer code which enables rigid-body, global minimum energy searches for molecular aggregation or alignment.

Comparison of simulation and experimental results for a model aqueous tert-butanol solution.

Molecular dynamics simulations are used to investigate the behavior of aqueous tert-butanol (TBA) solutions for a range of temperatures, using the CHARMM generalized force field (CGenFF) to model TBA and the TIP4P/2005 or TIP4P-Ew water model. Simulation results for the density, isothermal compressibility, constant pressure heat capacity, and self-diffusion coefficients are in good accord with experimental measurements. Agreement with the experiment is particularly good at low TBA concentration, where experiments have revealed anomalies in a number of thermodynamic properties. Importantly, the CGenFF model does not exhibit liquid-liquid demixing at temperatures between 290 and 320 K (for systems of 32 000 molecules), in contrast with the situation for several other common TBA models [R. Gupta and G. N. Patey, J. Chem. Phys. 137, 034509 (2012)]. However, whereas real water and TBA are miscible at all temperatures where the liquid is stable, we observe some evidence of demixing at 340 K and above. To evaluate the structural properties at low concentrations, we compare with both neutron scattering and recent spectroscopic measurements. This reveals that while the CGenFF model is a definite improvement over other models that have been considered, the TBA molecules still exhibit a tendency to associate at low concentrations that is somewhat stronger than that indicated by experiments. Finally, we discuss the range and decay times of the long-range correlations, providing an indication of the system size and simulation times that are necessary in order to obtain reliable results for certain properties.

Changes in the hydration structure of imidazole upon protonation: Neutron scattering and molecular simulations

The imidazole motif is widely encountered in biomolecules, and its biological role, for instance, as a proton relay, is often linked to its ability to form hydrogen bonds with water molecules. The detailed characterization of the hydration pattern of imidazole and of its changes upon protonation is thus of high interest. Here, we combine neutron scattering experiments with force field simulations to provide an unprecedented characterization of the neutral and protonated imidazole solvation at the atomistic level. We show that neutron diffraction data can be used to assess the quality of the imidazole force field in molecular simulations. Simulations using the CHARMM general force field for imidazole are in excellent agreement with the experimental neutron scattering data and we use them to provide an atomic scale interpretation of the neutron scattering patterns. Upon protonation, we clearly identify the signature of the reorganization in the hydration pattern caused by the change from one H-bond donor and one H-bond acceptor group for imidazole to two H-bond donor groups for imidazolium. We also point the limits of the experiment, which are rather insensitive to details of the H-bond geometry at the deprotonated nitrogen of imidazole and further complement the description of the hydration structure with ab initio molecular dynamics simulations.

Developing and Validating a Set of All-Atom Potential Models for Sodium Dodecyl Sulfate.

We present a set of novel all-atom potential models for sodium dodecyl sulfate (SDS), developed within the framework of the widely used OPLS-AA and General AMBER force fields. The choice of the parameters for the models is made by rigorously following the methodology of the used force fields to ensure full compatibility with the models for other compounds. For the GAFF model, extensive quantum-chemical computations are performed to obtain reliable Boltzmann-averaged atomic point charges, and the latter are compared with the single-conformation charges. For representation of the hydrocarbon tail, we use recently published improved parameters that correctly reproduce the properties of lipids and long alkanes. The models are validated on the basis of correct reproduction of the main properties of micelles (size, degree of counterion binding) as well as diffusion coefficient of the SDS monomer. As an extended test, a simulation of a micelle with a high aggregation number (382) and unnatural initial shape is performed, and a restructuring to the correct shape is observed. This proves the suitability of the developed models for simulations of concentrated SDS solutions containing large micelles and also emphasizes importance of hydrocarbon tail parameters for the micelle properties. Finally, the developed DS- models are tested in combination with several common Na+ and water models. Their effect on the properties of SDS micelles is discussed, and suitable combinations are determined.

The IDP-Specific Force Field ff14IDPSFF Improves the Conformer Sampling of Intrinsically Disordered Proteins.

Intrinsically disordered proteins (IDPs) or intrinsically disordered regions do not have a fixed tertiary structure but play key roles in signal regulation, molecule recognition, and drug targeting. However, it is difficult to study the structure and function of IDPs by traditional experimental methods because of their diverse conformations. Limitations of current generic protein force fields and solvent models were reported in the previous simulations of IDPs. We have also explored overcoming these limitations by developing the ff99IDPs and ff14IDPs force fields to correct the dihedral distribution for eight disorder-promoting residues often observed in IDPs and found encouraging improvements. Here we extend our correction of backbone dihedral terms to all 20 naturally occurring amino acids in the IDP-specific force field ff14IDPSFF to further improve the quality of the modeling of IDPs. Extensive tests of seven IDPs and 14 unstructured short peptides show that the simulated Cα chemical shifts obtained with the ff14IDPSFF force field are in quantitative agreement with those from NMR experiments and are more accurate than those obtained with the base generic force field and also our previous ff14IDPs that only corrects the eight disorder-promoting amino acids. The influence of the solvent model was also investigated and found to be less important. Finally, our explicit-solvent MD simulations further show that ff14IDPSFF can still be used to model structural and dynamical properties of two tested folded proteins, with a slightly better agreement in the loop regions for both structural and dynamical properties. These findings confirm that the newly developed IDP-specific force field ff14IDPSFF can improve the conformer sampling of intrinsically disordered proteins.

Internal rotation and equilibrium structure of the 2-methyl-2-nitropropane molecule from joint processing of gas phase electron diffraction data, vibrational and microwave spectroscopy data, and quantum chemical calculation results

The structure and internal rotation of the 2-methyl-2-nitropropane molecule is studied by electron diffraction and quantum chemical calculations with the use of microwave and vibrational spectroscopy data. The electron diffraction data are analyzed within the general intramolecular anharmonic force field model and the quantum chemical pseudoconformer model, considering the adiabatic separation of the degree of freedom of large amplitude motion, i.e., the internal rotation of the NO2 group. The equilibrium eclipsed configuration of the C s symmetry molecule has the following experimental bond lengths and valence angles: r e(N=O) = 1.226//1.226(8) A, r e(C–N)//r e(C–C) = 1.520//1.515/1,521(4) A, ∠еC–C–N = = 109.1/106,1(8)°, ∠еO=N=O = 124.2(6)°, ∠eC–C–Havg = 110(3)°. The equilibrium geometry parameters are well consistent with MP2/cc-pVTZ quantum chemical calculations and microwave spectroscopy data. The thermally average parameters previously obtained within the small vibration model show a satisfactory agreement with the new results. The electron diffraction data used in this work do not allow a reliable determination of the barrier to internal rotation. However, at a barrier of 203(2) cal/mol, which is derived from the microwave study, it follows from the electron diffraction data that the equilibrium configuration must correspond to an eclipsed arrangement of C–C and N=O bonds, which is also consistent with the results of quantum chemical calculations of various levels.

The right isotherms for the right reasons? Validation of generic force fields for prediction of methane adsorption in metal-organic frameworks

In recent years, the use of computational tools to aid in the evaluation, understanding and design of advanced porous materials for gas storage and separation processes has become evermore widespread. High-performance computing facilities have become more powerful and more accessible and molecular simulation of gas adsorption has become routine, often involving the use of a number of default and commonly used parameters as a result. In this work, we consider the application of molecular simulation in one particular field of adsorption – the prediction of methane adsorption in metal-organic frameworks in the low loading regime – and employ a range of computational techniques to evaluate the appropriateness of many commonly chosen simulation parameters to these systems. In addition to confirming the power of relatively simple generic force fields to quickly and accurately predict methane adsorption isotherms in a range of MOFs, we demonstrate that these force fields are capable of providing detailed molecular-level information which is in very good agreement with quantum chemical predictions. We highlight a number of chemical systems in which molecular-level insight from generic force fields should be approached with a degree of caution and provide some general recommendations for best practice in simulations of CH4 adsorption in MOFs.

Modeling of adsorption of CO2 in the deformed pores of MIL-53(Al).

Molecular simulations were performed to predict CO2 adsorption in flexible metal-organic frameworks (MOFs). A generic force field was fitted to our experimental data to describe the non-bonded (electrostatic and van der Waals) interactions between CO2 molecules and the large pore (lp) and narrow pore (np) forms of the MIL-53(Al) framework. With the new validated force field, it is possible to predict CO2 uptake and enthalpy of adsorption at various applied external pressures that will modify the structure's pore configuration and allow us to have more control over the adsorption/desorption process. A sensitivity analysis of MOF adsorption properties to the variation of the force field parameters was also intensively studied. It was shown that relatively small variations of the adsorbate gas model can improve the quality of the numerical predictions of the experimental data. However, the variations must be kept small enough to not modify the properties of the gas itself.

CHARMM-GUI Ligand Reader & Modeler

Reading ligand structures into any simulation program is often very difficult and time consuming, as the corresponding molecular force field parameters or structure files may not be available immediately. To resolve this issue and simplify the ligand model preparation, we have developed Ligand Reader & Modeler in CHARMM-GUI. Users can upload ligand structure information to the server in various ways (using PDB ID, ligand ID, SMILES, MOL/MOL2/SDF file, and PDB file), and the uploaded structure will be displayed on the sketchpad for verification and further modification. Ligand Reader & Modeler will prepare the ligand force filed parameters and necessary structure files by searching for the ligand in the entire CHARMM force field library or using CHARMM General Force Field (CGenFF). In addition, a user can draw chemical substitution sites and substituents in each attachment site to generate a set of combinatorial structure files and corresponding force field parameters for high-throughput screening simulation. Finally, the output can be used in other CHARMM-GUI modules to build a simulation system for all supported simulation programs such as CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, and OpenMM.

A novel method for calculating relative free energy of similar molecules in two environments

Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy, simple implementation, robustness and efficiency, which prevent the calculations from being automated and limit their use. Here we present an exact and complete decoupling analysis in which the partition functions of the compared systems decompose into the partition functions of the common and different subsystems. This decoupling analysis is applicable to submolecules with coupled degrees of freedom such as the methyl group and to any potential function (including the typical dihedral potentials), enabling to remove less terms in the transformation which results in a more efficient calculation. Then we show mathematically, in the context of partition function decoupling, that the two compared systems can be simulated separately, eliminating the need to design a composite system. We demonstrate the decoupling analysis and the separate transformations in a relative free energy calculation using MD simulations for a general force field and compare to another calculation and to experimental results. We present a unified soft-core technique that ensures the monotonicity of the numerically integrated function (analytical proof) which is important for the selection of intermediates. We show mathematically that in this soft-core technique the numerically integrated function can be non-steep only when we transform the systems separately, which can simplify the numerical integration. Finally, we show that when the systems have rugged energy landscape they can be equilibrated without introducing another sampling dimension which can also enable to use the simulation results for other free energy calculations.

Full-atomistic simulations of poly(ϵ-caprolactone) diol models with CVFF and CGenFF

Poly(ϵ-caprolactone) (PCL) diol, with good biodegradation and biocompatibility, is one of the widely used soft segments (SSs) in composing bio-polyester-urethanes (Bio-PUs), which show great potential in both biomedical and tissue engineering applications. Properties of Bio-PUs are tunable by combining SS monomers with different molecular weights, structures, modifications, and ratio of components. Although numbers of research have reported many Bio-PUs properties, few studies have been done at the molecular scale. In this study, we use molecular dynamic (MD) simulation to construct atomistic models for two commonly used PCL diol SSs with different molecular weights 1247.58 Da and 1932.42 Da. We compare the simulation results by using two widely used classical force fields for organic molecules: Consistent Valence Force Field (CVFF) and CHARMM General Force Field (CGenFF), and discuss the validity and accuracy. Melt density, volume, polymer conformations, transition temperature, and mechanical properties of PCL diols are calculated and compared with experiments. Our results show that both force fields provide accurate predictions on the properties of PCL diol system at the molecular scale and could help the design of future Bio-PUs.

Absolute binding free energy calculations of CBClip host-guest systems in the SAMPL5 blind challenge.

Herein, we report the absolute binding free energy calculations of CBClip complexes in the SAMPL5 blind challenge. Initial conformations of CBClip complexes were obtained using docking and molecular dynamics simulations. Free energy calculations were performed using thermodynamic integration (TI) with soft-core potentials and Bennett's acceptance ratio (BAR) method based on a serial insertion scheme. We compared the results obtained with TI simulations with soft-core potentials and Hamiltonian replica exchange simulations with the serial insertion method combined with the BAR method. The results show that the difference between the two methods can be mainly attributed to the van der Waals free energies, suggesting that either the simulations used for TI or the simulations used for BAR, or both are not fully converged and the two sets of simulations may have sampled difference phase space regions. The penalty scores of force field parameters of the 10 guest molecules provided by CHARMM Generalized Force Field can be an indicator of the accuracy of binding free energy calculations. Among our submissions, the combination of docking and TI performed best, which yielded the root mean square deviation of 2.94kcal/mol and an average unsigned error of 3.41kcal/mol for the ten guest molecules. These values were best overall among all participants. However, our submissions had little correlation with experiments.