Comparison of SCC-DFTB and NDDO-Based Semiempirical Molecular Orbital Methods for Organic Molecules

Sattelmeyer, Kurt W.; Tirado‐Rives, Julian; Jorgensen, William L.

doi:10.1021/jp064544k

Cited by 135 publications

(237 citation statements)

References 44 publications

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“…Before the SCF begins, a typical program would also pre-compute the symmetric orthogonalization matrix S −1/2 from the overlap matrix, as this would be needed to transform the generalized eigenvalue problem [Eq. (6)] into a standard eigenvalue problem within every SCF cycle. This operation scales cubically with respect to the number of AOs; however, for a system of 5-15 heavy atoms with a 1s1p AO basis, its calculation requires approximately the same wall clock time as it does to compute all of the mapping coefficients with a 1D auxiliary basis (not just those for a pair of atoms).…”

Section: E Computational Effortmentioning

confidence: 99%

“…[1][2][3][4] Although SCC-DFTB has proven to be a very useful semiempirical model, [5][6][7][8] there remain open questions as to which theoretical developments will result in the most beneficial improvements. 3 For example, one of the recent improvements 4,9 introduced charge-dependent corrections through the inclusion of higher-order expansion terms, i.e., beyond second-order; however, in a recent work, 10 we explored the theory and approximations used in de novo density-functional expansion methods and concluded that a second-order potential energy expansion reproduces standard density functional theory (DFT) results extremely well if the model is not encumbered by the following approximations: (1) the two-body treatment of the first-order matrix elements, (2) the Slater monopole auxiliary basis representation of the response density, and (3) the limited size of the orbital basis.…”

Section: Introductionmentioning

confidence: 99%

“…By using this type of auxiliary basis, SCC-DFTB avoids the need for computing threeand four-center electron repulsion integrals, and Mulliken partitioning allows for the rapid construction of the auxiliary density from the atomic orbital (AO) density matrix through spline evaluation of the precomputed overlap matrices; however, this crude representation of the response density can have adverse effects on electrostatic interactions. 21 In general, accurate electrostatics are important for intermolecular 22,23 Variations of the SCC-DFTB method have been applied to water clusters, 24 liquid water, 24 and organic molecules, 6 and limitations in hydrogen bonding were noted in many cases, although it is difficult to directly attribute these deficiencies solely to the electrostatic description.…”

Section: Introductionmentioning

confidence: 99%

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Density-functional expansion methods: Generalization of the auxiliary basis

Giese¹,

York²

2011

The Journal of Chemical Physics

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The formulation of density-functional expansion methods is extended to treat the second and higherorder terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the selfconsistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

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Section: E Computational Effortmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Density-functional expansion methods: Generalization of the auxiliary basis

Giese¹,

York²

2011

The Journal of Chemical Physics

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“…The M062X functional appears to offer comparable isomerization energy prediction performance to the best performing currently available dispersion corrected functionals against this benchmark dataset.The performance of various levels of quantum chemical methods for estimating the isomerization energies (∆ isom E) and enthalpies (∆ isom H) of organic compounds has been the focus of a number of investigations over the past several years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This attention is primarily driven by the poor performance of many popular density functionals -most notably the B3LYP functional -with regard to these types of intramolecular rearrangements.…”

mentioning

confidence: 99%

Performance of the M062X density functional against the ISOL set of benchmark isomerization energies for large organic molecules

Rayne

Forest

2010

Nat Prec

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Gas phase standard state (298.15 K, 1 atm) isomerization energies (∆ isom E) were calculated using the M062X functional with the QZVP, 6-311++G(d,p), 6-311++G(2d,2p), and cc-pVTZ basis sets against the 24 reactions in the ISOL set of benchmark isomerization energies for large organic molecules. The M062X functional appears to offer comparable isomerization energy prediction performance to the best performing currently available dispersion corrected functionals against this benchmark dataset.The performance of various levels of quantum chemical methods for estimating the isomerization energies (∆ isom E) and enthalpies (∆ isom H) of organic compounds has been the focus of a number of investigations over the past several years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This attention is primarily driven by the poor performance of many popular density functionals -most notably the B3LYP functional -with regard to these types of intramolecular rearrangements. Several new types of functionals and corrections have been developed in response to these reported theoretical shortcomings. However, prior ∆ isom H/∆ isom E benchmarking efforts have concentrated on relatively small molecules (<8 heavy atoms).Recently, Huenerbein et al. [15] have proposed the ISOL set of 24 isomerization reactions for large organic compounds (Figure 1). In their benchmarking study, the authors obtained reference ∆ isom E at the SCS-MP3/CBS level on B97D/TZVP optimized structures. Based on previous efforts showing the M062X density functional performs well for computing ∆ isom H/∆ isom E of smaller organic molecules [6,[10][11][12], in the current work we assess the performance of this functional for calculating ∆ isom E for the ISOL benchmark set.Single point calculations were performed using Gaussian 09 [16] and the M062X density functional [17] with the QZVP [18], 6-311++G(d,p) and 6-311++G(2d,2p) [19][20][21][22][23], and cc-pVTZ [24,25] basis sets on the B97D/TZVP optimized geometries from the ISOL set in Huenerbein et al. [15], and corresponding ∆ isom E were calculated along with associated method specific error metrics against the reference SCS-MP3/CBS ∆ isom E (Table 1) (QZVP,p), and 6-311++G(2d,2p)) or two (cc-pVTZ) outliers present with maximum absolute deviations ranging from 13.8 to 17.8 kcal mol −1 depending on the basis set, also similar to that of the PBE0 (MAXD=9.1 kcal mol −1 ; 0 outliers), B2GP-PLYP-D (MAXD=11.5 kcal mol −1 ; 1 outlier), BMK-D (MAXD=17.1 kcal mol −1 ; 1 outlier), and PW6B95-D (MAXD=11.9 kcal mol −1 ;

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“…2 The SCC-DFTB method has been shown to yield calculated heats of formation mean averaged errors (MAE) somewhat between AM1 and PM3, and much larger than PDDG/PM3, due to an over stabilization of molecules containing S-O bonds. 1 On the other hand, small peptides' relative energies and structures calculated with the SCC-DFTB method are in good agreement with B3LYP/6-31G* density functional theory 106 and ab initio MP2/6-31G* 10 calculations, at a much lower computational cost. In a study of H-bonded systems, 107 it was shown that SCC-DFTB underestimates the H-bond distances in comparison to B3LYP/6-31G*, but those energies are somewhat improved by considering the waters as classical (TIP3P) in a QM/MM scheme.…”

Section: Resultsmentioning

confidence: 54%

Are Current Semiempirical Methods Better Than Force Fields? A Study from the Thermodynamics Perspective

2009

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The semiempirical Hamiltonians MNDO, AM1, PM3, RM1, PDDG/MNDO, PDDG/PM3, and SCC-DFTB, when used as part of a hybrid QM/MM scheme for the simulation of biological molecules, were compared on their abilities to reproduce experimental ensemble averages at or near room temperatures for the model system alanine dipeptide in water. Free energy surfaces in the (φ, ψ) dihedral angle space, 3 J(H N ,H R ) NMR dipolar coupling constants, basin populations, and peptide-water radial distribution functions (RDF) were calculated from replica exchange simulations and compared to both experiment and fully classical force field calculations using the Amber ff99SB force field. In contrast with the computational chemist's intuitive idea that the more expensive a method the better its accuracy, the ff99SB force field results were more accurate than most of the semiempirical methods, with the exception of RM1. None of the methods, however, was able to accurately reproduce the experimental data. Analysis of the results indicate that the specific QM/MM interactions have little influence on the sampling of free energy surfaces, and the differences are well explained simply by the intrinsic properties of the various QM methods.

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Comparison of SCC-DFTB and NDDO-Based Semiempirical Molecular Orbital Methods for Organic Molecules

Cited by 135 publications

References 44 publications

Density-functional expansion methods: Generalization of the auxiliary basis

Density-functional expansion methods: Generalization of the auxiliary basis

Performance of the M062X density functional against the ISOL set of benchmark isomerization energies for large organic molecules

Are Current Semiempirical Methods Better Than Force Fields? A Study from the Thermodynamics Perspective

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