The ethanol molecule showing the atom numbering that will be used throughout.
Flow chart showing the seven steps involved in the design of the polarizable flexible ethanol model.
Statistics on the electric fields collected during the MD simulation using the flexible, nonpolarizable model of ethanol by Chen et al. (Ref. 29). Panels (a)–(c) each summarize 200 000 measurements of the electric field on C(3), O(2), and H(1), respectively. Panels (d)–(f) show the corresponding distributions for the 618 selected electric fields. The fields are given in reduced units, to convert .
A comparison of the Coulomb overlap (solid line) evaluated from Eq. (5) with (dotted line) and the approximate form for from Eq. (7) (dashed line). Results for O(2)–C(3) and H(1)–O(2) atomic pairs are shown in (a) and (b), respectively.
The impact of the representation of the interatomic Coulomb interaction, . The H(1)H(1) radial distribution is shown for bulk ethanol at and . Results for the fCINTRA model with the overlap integral [Eq. (5)] form of the Coulomb interaction are given by a solid line, while use of Eq. (7) leads to the distribution identified by the dotted line.
The torsional potential, , between H(1)–O(2)–C(3)–C(4) as a function of the dihedral angle. For convenience, each vertical scale is shifted so that the ab initio curve minimum corresponds to an energy of zero. The results are shown with open circles, corrected ab initio results are open squares, and least-squares fits to the corrected ab initio results are filled squares. The sequence of panels shows the dependence of the potential on the field. In reduced units: (a) , , ; (b) , , ; (c) , , ; (d) , , ; (e) , , ; and (f) , , .
The torsional potential, , between O(2)–C(3)–C(4)–H(5) as a function of the dihedral angle. For convenience, each vertical scale is shifted so that the ab initio curve minimum corresponds to an energy of zero. The results are shown with open circles, corrected ab initio results are open squares, and the field-independent fit to the corrected ab initio results are filled squares. The panels show the dependence of the potential on the field. In reduced units: (a) , , ; (b) , , ; (c) , , ; (d) , , ; (e) , , ; and (f) , , .
The impact of charge “mass” on the diffusion coefficient and radial distribution functions obtained from simulations. The final mass chosen for the simulations is identified by (a). The diffusion coefficients are plotted against the logarithm of the charge mass [in units of ]. Radial distributions are given for four masses, identified with (a)–(d).
The energy components and the conserved quantity as a function of time. The potential energy includes all contributions except for the intramolecular potential which is shown separately. The kinetic energy for the charges is effectively zero throughout the simulation.
The impact of damping on the range of parameter values allowed in the simulation. The solid line shows the ratio of the damped coefficient to the original [see Eqs. (23)–(26)].
A comparison of radial distributions in bulk ethanol obtained from experiment, a nonpolarizable model, and the fCINTRA polarizable model. The solid, dotted, and dashed lines correspond to the fCINTRA model, the OPLS model, and the experimental (Ref. 7) curves, respectively. The topmost panel shows the distribution between hydrogen-bonding hydrogens. The lower panels include multiple contributions from O(2), C(3), and C(4), as discussed in Sec. III A.
Snapshots of bulk ethanol from the fCINTRA polarizable, flexible model. All atoms appear in the snapshot on the right, while the center snapshot emphasizes O(2) and H(1), and the rightmost snapshot shows the carbons and their hydrogens.
Average error in the dipole moment, relative to MP2/aug-cc-pVTZ reference calculations [see Eq. (2)], for ethanol in 16 electric fields. Errors are reported for four functionals and five basis sets.
Charge fluctuation parameters [see Eq. (3)] and Lennard-Jones parameters for the polarizable, flexible fCINTRA ethanol model. The fCINTRA parameters are compared with polarizable CHARMM (Ref. 22) values. For comparisons with CHARMM, the have been shifted to give a H(1) value of zero in the sixth column. are given in and are reported in . The LJ parameters for H(1) and O(2) were optimized for the fCINTRA model while the remaining values are from CHARMM (Ref. 22).
The zero-field bond stretching constants and the field dependence of the equilibrium bond lengths [see Eq. (10)] extracted from calculations of ethanol. identifies the bond: the superscripts follow the atom numbering shown in Fig. 1, while the subscripts are added for convenience and identify the atom types. is the bond stretching force constant and is the corresponding zero-field equilibrium bond length. The terms and the coefficients are given for each bond length. The minimum and maximum bond lengths observed in the 618 fields are provided in the fourth and fifth rows, respectively. The fields used to calculate the terms are in . Note that .
The zero-field angle bending force constant and the field dependence of the equilibrium bond angles [see Eq. (11)] extracted from calculations of ethanol. The terms and the coefficients are given for each bend. The minimum and maximum bond angles observed in the 618 fields are provided in the fourth and fifth rows, respectively. The fields used to calculate the terms are in . Note that .
Field dependence of the torsional coefficients for rotation about the C(3)–O(2) bond in ethanol [see Eq. (12)]. The minimum and maximum values for the coefficients in 618 fields are given in the second and third rows, respectively. The third row gives the coefficients in the absence of a field and the following rows list the field-dependent terms. The fields used to calculate the terms are in . Note that .
Properties of bulk ethanol as predicted from the polarizable, flexible fCINTRA model are compared with experiment. Values for the polarizable OPLS (Ref. 12), PIPF (Ref. 11), and Drude (Ref. 13) models and for the nonpolarizable OPLS (Ref. 10) model are included. The second column reports the average oxygen charge from the simulations. The OPLS-pol, PIPF, and Drude models do not introduce polarization directly into the charge so the tabulated values correspond to the zero-field limit. The third, fifth, and seventh columns report peak positions (PPs) in the interatomic distributions. For experiment, this work, and OPLS, X represents the total contribution from O(2), C(3), and C(4). The peak positions for the polarizable OPLS and PIPF models correspond only to oxygen . Corresponding coordination numbers (CN) are given in the fourth and sixth columns. The self-diffusion coefficient is given in the eighth column, while the dielectric constant, the average dipole moment, and enthalpy of vaporization are given in the following columns. The seventh row identifies the quantities obtained with a fluctuating charge model but a zero-field intramolecular potential. Likewise, the following row refers to the fixed charge limit, with a field-dependent intramolecular potential. The final row (“E shift”) corresponds to the field-dependent charges and intramolecular potential implemented with an omitted force contribution.
Hydrogen bond statistics evaluated from snapshots of the simulation cell. A chain is defined by a series of hydrogen bonds, the percentage of single molecules identifies the average number of molecules that are not hydrogen bonding, and branches correspond to molecules that simultaneously hydrogen bond to three others.
Article metrics loading...
Full text loading...