**"Accurate Partial Atomic Charges for High-Energy Molecules Using
Class IV Charge Models with the MIDI! Basis Set," C. P. Kelly, C. J.
Cramer, and D. G. Truhlar, Theoretical Chemistry Accounts, 113, 133-151 (2005).**

Abstract. We have recently developed a new class IV charge model for calculating partial atomic charges in molecules. The new model, called charge model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree–Fock theory and by hybrid density functional theory (HDFT) based on the modified Perdew–Wang density functional with several basis sets. In the present article, we extend CM3 for calculating partial atomic charges by Hartree–Fock theory with the economical but well balanced MIDI! basis set. Then, using a test set of accurate dipole moments for molecules containing nitramine functional groups (which include many high-energy materials), we demonstrate the utility of several parameters designed to improve the charges in molecules containing both N and O atoms. We also show that one of our most recently developed CM3 models that is designed for use with wave functions calculated at the mPWXPW91/MIDI! level of theory (where X denotes a variable percentage of Hartree–Fock exchange) gives accurate charge distributions in nitramines without additional parameters for N and O. To demonstrate the reliability of partial atomic charges calculated with CM3, we use these atomic charges to calculate polarization free energies for several nitramines, including the commonly used explosives 1,3,5-trinitro-s-triazine (RDX) and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW), in nitromethane. These polarization energies are large and negative, indicating that electrostatic interactions between the charge distribution of the molecule and the solvent make a large contribution to the free energy of solvation of nitramines. By extension, the same conclusion should apply to solid-state condensation. Also, in contrast to some other charge models, CM3 yields atomic charges that are relatively insensitive to the presence of buried atoms and small conformational changes in the molecule, as well as to the level of treatment of electron correlation. This type of charge model should be useful in the future development of solvation models and force fields designed to estimate intramolecular interactions of nitramines in the condensed phase.

**"A Class IV Charge Model for Boron Based on Hybrid Density
Functional Theory," J. M. Brom, B. J. Schmitz, J. D. Thompson, C. J. Cramer,
and D. G. Truhlar, Journal of Physical Chemistry A, 107, 6483-6488.**

Abstract. We present a class IV charge model, in particular charge model 3 (CM3), for molecules containing boron. The model is designed to be able to obtain particularly useful partial atomic charges by mapping (class II) partial atomic charges obtained by Löwdin population analysis into improved (class IV) charges that reproduce accurate charge-dependent observables. To train the model, we mainly use dipole moments as the observables, and we have developed a training set of 43 accurate dipole moments and one quadrupole moment for molecules containing B in addition to H, C, N, O, and/or F. In the present paper we report CM3 parameters for use with hybrid density functional theory, in particular with Adamo and Barone's modified Perdew-Wang (mPW) gradient-corrected exchange functional, the PW91 gradient-corrected correlation functional, 25% Hartree-Fock exchange, and the popular 6-31G* basis set. Dipole moments of boron-containing molecules computed from CM3 atomic point charges have root-mean-square errors of only 0.13 D and mean unsigned errors of 0.10 D as compared to experiment or high level of theory.

**"Parameterization of Charge Model 3 for AM1, PM3, BLYP, and B3LYP,"
J. D. Thompson, C. J. Cramer, and D. G. Truhlar, Journal of Computational
Chemistry, 24, 1291-1304 (2003).**

Abstract. We have recently developed a new Class IV charge model for calculating partial atomic charges in molecules. The new model, called Charge Model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree-Fock theory and by hybrid density functional theory (DFT) based on the modified Perdew-Wang density functional with several basis sets. In the present article we extend CM3 to semiempirical molecular orbital theory, in particular Austin Model 1 (AM1) and Parameterized Model 3 (PM3), and to the popular BLYP and B3LYP DFT and hybrid DFT methods, respectively. For the BLYP extension, we consider the 6-31G(d) basis set, and for the B3LYP extension, we consider three basis sets: 6-31G(d), 6-31+G(d), and MIDI!6D. We begin with the previous CM3 strategy, which involves 34 parameters for 30 pairs of elements. We then refine the model to improve the charges in compounds that contain N and O. This modification, involving two new parameters, leads to improved dipole moments for amides, bifunctional H, C, N, O compounds, aldehydes, ketones, esters, and carboxylic acids; the improvement for compounds not containing N results from obtaining more physical parameters for carbonyl groups when the OCN conjugation of amides is addressed in the parameterization. In addition, for the PM3 method, we added an additional parameter to improve dipole moments of compounds that contain bonds between C and N. This additional parameter leads to improved accuracy in the dipole moments of aromatic nitrogen heterocycles with five-membered rings.

**"More Reliable Partial Atomic Charges When Using Diffuse Basis
Functions," J. D. Thompson, J. D. Xidos, T. M. Sonbuchner, C. J. Cramer, and
D. G. Truhlar, PhysChemComm 5 (18), 117-134
http://dx.doi.org/10.1039/b206369g (2002).**

Abstract. We present a method that alleviates some of the sensitivity to the inclusion of diffuse basis functions when calculating partial atomic charges from a Löwdin population analysis. This new method locally redistributes that part of the Löwdin population that comes from diffuse basis functions so that the final charges closely resemble those calculated without diffuse functions. We call this method the redistributed Löwdin population analysis (RLPA). The method contains one parameter for each atomic number, and we optimized the parameter for the 6-31+G(d) basis set. The method has been tested on compounds that contain H, Li, C, N, O, F, Si, P, S, Cl, and Br. For a test set of 398 compounds with experimental and high-level theoretical dipole moments, the dipole moments derived from the charges obtained by standard Löwdin population analysis have errors 35% larger than those obtained by the corresponding RLPA using the same basis set. In judging the quality of the RLPA with respect to the test set of dipole moments, we have also found that dipole moments derived from Mulliken population analysis have errors 120% larger than those derived from RLPA for the same basis set. The new method is particularly successful for the 207 systems containing only first row atoms (H, C, N, O, F) for which the errors in the dipole moments computed from the partial atomic charges obtained by standard Löwdin and Mulliken analysis are respectively 115 and 419% larger than those obtained by RLPA.

**"Charge Model 3: A Class IV Charge Model Based on Hybrid Density
Functional Theory with Variable Exchange," P. Winget, J. D. Thompson, J. D.
Xidos, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry A 106,
10707-10717 (2002).**

Abstract. We present a new class IV charge model. The model, called Charge Model 3 (CM3), is designed to be able to obtain accurate partial charges from hybrid density functional calculations with a variable amount of Hartree-Fock exchange and with or without diffuse functions in the basis. The model maps atomic partial charges obtained by Löwdin or redistributed Löwdin population analysis into improved (class IV) charges that reproduce accurate charge-dependent observables for molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br. The hybrid density functional theory we use here is based on Adamo and Barone's modified Perdew-Wang (mPW) gradient-corrected exchange functional and the PW91 gradient corrected correlation functional. These parametrizations can be used with any arbitrary fraction of Hartree-Fock exchange in conjunction with any of the five basis sets, MIDI!, MIDI!6D, 6-31G*, 6-31+G*, and 6-31+G**. We also present two parametrizations for Hartree-Fock theory employing the MIDI!6D and 6-31G* basis sets. Dipole moments computed from CM3 atomic point charges have root-mean-square errors between 0.26 and 0.40 D and mean unsigned errors in the range 0.19-0.28 D compared to experiment.

**"MIDIX Basis Set for Lithium Atom: Accurate Geometries and Atomic Partial
Charges for Lithium Compounds with Minimal Computational Cost," J. D.
Thompson, P. Winget, and D. G. Truhlar, PhysChemComm, 4 (16), 72-77
http://dx.doi.org/10.1039/b105076c . Supplementary information:
http://www.rsc.org/suppdata/qu/b1/b105076c (2001).**

Abstract. We present a MIDIX basis set for Li that accurately predicts geometries, charge distributions, and partial atomic charges for a test set of compounds at a reasonable cost. MIDIX basis sets, which are also called MIDI!, are heteroatom-polarized split-valence basis sets in which the polarization functions are optimized in order to predict realistic molecular geometries and atomic partial charges. The MIDIX basis set uses the core, inner valence, and outer valence basis functions of the MIDI basis set plus an additional Gaussian basis function. We optimized the p exponent to obtain realistic predictions of geometry, density dipole moments, and Löwdin dipole moments at the Hartree–Fock and hybrid density functional levels of theory, using the mPW1PW91 hybrid density functional for the latter. The MIDIX basis set predicts Hartree–Fock geometries and Hartree–Fock and hybrid density functional Löwdin dipole moments more accurately than either the 3-21G(d) or 6-31G(d) basis set for most of the compounds in our training set. It also predicts more accurate Hartree–Fock and hybrid density functional density dipole moments than the 3-21G(d) basis set. The present results show that the basis set is expected to be very useful for calculating geometries and electrostatic properties of lithium compounds containing H, C, N, O, F, Si, P, S, Cl, Br, and I, especially organolithium and lithium-sulfur compounds.

**"Class IV Charge Models: A New Semiempirical
Approach in Quantum Chemistry," J. W. Storer, D. J. Giesen, C. J. Cramer,
D. G. Truhlar, Journal of Computer-Aided Molecular Design, 9, 87-110 (1995).**

Abstract. We propose a new criterion for defining partial charges
on atoms in molecules, namely that physical observables calculated from
those partial charges should be as accurate as possible. We also propose
a method to obtain such charges based on a mapping from approximate electronic
wave functions. The method is illustrated by parameterizing two new charge
models called AM1-CM1A and PM3-CM1P, based on experimental dipole moments
and, respectively, on AM1 and PM3 semiempirical electronic wave functions.
These charge models yield root-mean-square errors of 0.30 and 0.26 Debyes
respectively in the dipole moments of 195 neutral molecules consisting
of 103 molecules containing H, C, N, and O covering variations of multiple
common organic functional groups, and 68 fluorides, chlorides, bromides,
and iodides, 15 compounds containing H, C, Si or S, and 9 compounds containing
C-S-O or C-N-O linkages. In addition, partial charges computed with this
method agree extremely well with high level *ab initio* calculations
for both neutral compounds and ions. The CM1 charge models provide a more
accurate point charge representation of the dipole moment than provided
by most previously available partial charges, and they are far less expensive
to compute.

**"The MIDI! Basis Set for Quantum Mechanical Calculations of
Molecular Geometries and Partial Charges," R. Evan Easton, David J. Giesen,
Andrew Welch, Christopher J. Cramer, and Donald G. Truhlar, Theoretica
Chimica Acta 93, 281-301 (1996).**

Abstract. We present a series of calculations designed to identify an economical basis set for geometry optimizations and partial charge calculations on medium-size molecules, including neutrals, cations, and anions, with special emphasis on functional groups that are important for biomolecules and drug design. A new combination of valence basis functions and polarization functions, called the MIDI! basis set, is identified as a good compromise of speed and accuracy, yielding excellent geometries and charge balances at a cost that is as affordable as possible for large molecules. The basis set is optimized for molecules containing H, C, N, O, F, P, S, and Cl. Although much smaller than the popular 6-31G* basis set, in direct comparisons it yields more accurate geometries and charges as judged compared to MP2/cc-pVDZ calculations.

You can download this basis set at the Basis
Set Database which is put together by the helpful people at the Pacific
Northwest Laboratory.

**"MIDI! Basis Set for Silicon, Bromine, and Iodine," J. Li, C. J.
Cramer, and D. G. Truhlar, Theoretical Chemistry Accounts 99, 192-196 (1998).**

Abstract. The MIDI! basis set is extended to three new
atoms: silicon, bromine, and iodine. The basis functions for these heteroatoms
are developed from the standard 3-21G basis set by adding one Gaussian-type
d subshell to each Si, Br, or I atom. The exponents of the d functions
are optimized to minimize errors in the geometries and charge distributions
that these basis functions yield when they are used in Hartree-Fock calculations
with all atoms represented by the MIDI! basis. The MIDI! basis is defined
to use five spherical d functions in a d subshell. We present a detailed
comparison of such calculations to calculations employing six Cartesian
d functions in each d subshell; these studies show that 5D and 6D options
give very similar results for molecular geometries and dipole moments.

**"A Class IV Charge Model for Molecular Excited States," J. Li, B.
Williams, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Physics
110, 724-733 (1999).**

Abstract. We present a new parameterization for calculating
class IV charges for molecules containing H, C, N, O, F, Si, P, S, Cl,
Br, and I from wave functions calculated at the intermediate-neglect-of-differential-overlap-for-spectroscopy
(INDO/S) level. First we readjust the oxygen parameters in INDO/S
on the basis of electronic excitation energies; this yields a new set of
parameters called INDO/S2. Then we parameterize the charge model.
The new model, called Charge Model 2 for INDO/S2 (CM2/INDO/S2), is parameterized
against the most accurate available data from both ab initio and experimental
sources for dipole moments of ground and excited electronic states.
For a training set containing 211 dipole moments of molecules in their
ground states and 33 dipole moments of molecules in their first excited
states, the CM2/INDO/S2 model leads to an RMS error in dipole moments of
0.26 D for ground states and 0.40 D for the excited states. The new
model, INDO/S2 with CM2, systematically improves the nÆp* excitation
energies and the dipole moments of the excited states of carbonyl compounds.
We also parameterized a CM2 model for the standard INDO/S model (CM2/INDO/S),
which predicts quite accurate dipole moments for ground states with an
RMS error of 0.24 D.

**"Accurate Dipole Moments from Hartree-Fock Calculations by Means
of Class IV Charges," J. Li, J. Xing, C. J. Cramer, and D. G. Truhlar,
Journal of Chemical Physics 111, 885-892 (1999).**

Abstract. Charge Model 2 (CM2) is parameterized for Hartree Fock
calculations with the correlation-consistent polarized valence double zeta
(cc-pVDZ) basis set. The resulting charge model has an RMS error of 0.18
D over a training set of 198 polar molecules. The charge model is additionally
applied to 8 nucleic acid bases and methyl azide to test its performance
for nitrogen-containing compounds not found in the training set. The results
demonstrate that this new CM2 model based on ab initio Hartree-Fock calculations
is robust in predicting the charge distributions of such molecules. Comparison
of CM2 results for the nitrogen-containing test set with those from a previous
charge model, Charge Model 1 (CM1) based on AM1 and PM3 wave functions,
indicate that the CM2 charges are more accurate than those from the previous
model.

*Last updated December 8, 2005*