Semiempirical Quantum Chemical Model Research Articles

Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results.

Quantum chemistry provides chemists with invaluable information, but the high computational cost limits the size and type of systems that can be studied. Machine learning (ML) has emerged as a means to dramatically lower the cost while maintaining high accuracy. However, ML models often sacrifice interpretability by using components such as the artificial neural networks of deep learning that function as black boxes. These components impart the flexibility needed to learn from large volumes of data but make it difficult to gain insight into the physical or chemical basis for the predictions. Here, we demonstrate that semiempirical quantum chemical (SEQC) models can learn from large volumes of data without sacrificing interpretability. The SEQC model is that of density-functional-based tight binding (DFTB) with fixed atomic orbital energies and interactions that are one-dimensional functions of the interatomic distance. This model is trained to ab initio data in a manner that is analogous to that used to train deep learning models. Using benchmarks that reflect the accuracy of the training data, we show that the resulting model maintains a physically reasonable functional form while achieving an accuracy, relative to coupled cluster energies with a complete basis set extrapolation (CCSD(T)*/CBS), that is comparable to that of density functional theory (DFT). This suggests that trained SEQC models can achieve a low computational cost and high accuracy without sacrificing interpretability. Use of a physically motivated model form also substantially reduces the amount of ab initio data needed to train the model compared to that required for deep learning models.

Neutral-to-ionic photoinduced phase transition of tetrathiafulvalene-p-chloranil by electronic and vibrational excitation: A real-time nuclear-electronic dynamics simulation study.

Tetrathiafulvalene-p-chloranil exhibits photoinduced phase transition (PIPT) between neutral (N) and ionic (I) phases, in which the constituent molecules are approximately charge-neutral and ionic, respectively. In addition to visible-light irradiation, which can induce both N → I and I → N PIPTs, infrared irradiation has been reported to induce the N → I PIPT. These results suggest that N → I and I → N PIPTs can be driven by electronic excitation, and the I → N PIPT can also be driven by vibrational excitation. However, the feasibility of the N → I PIPT using vibrational excitation remains an open question. In this study, we address this issue by simulating the PIPT processes using a nonadiabatic molecular dynamics approach combined with real-time electron dynamics at the level of a semiempirical quantum chemical model, density-functional tight binding. The results show the importance of vibronic interactions in the PIPT processes, thereby suggesting the possibility of N → I PIPT by vibrational excitations with infrared irradiation.

Relation between the Electronic Properties of Regioregular Donor-Acceptor Terpolymers and Their Binary Copolymers.

By analyzing the optical band gap and energy levels of seven different regioregular terpolymers in which two different electron-rich donor moieties are alternating with a common electron-deficient acceptor unit along the backbone, we establish a direct correlation with the properties of the corresponding binary copolymers in which one donor and one acceptor are combined. For this study, we use diketopyrrolopyrrole as the common acceptor and different π-conjugated aromatic oligomers as donors. We find that the optical band gap and frontier orbital energies of the terpolymers are the arithmetic average of those of the parent copolymers with remarkable accuracy. The same relationship is also found for the open-circuit voltage of the bulk heterojunction solar cells made with the ter- and copolymers in combination with [6,6]-phenyl-C71-butyric acid methyl ester. Comparison of these findings with data in the literature suggests that this is a universal rule that can be used as a tool when designing new π-conjugated polymers. The experimental results are supported by a semiempirical quantum chemical model that accurately describes the energy levels of the terpolymers after parametrization on the energy levels of the copolymers and also provides a theoretical explanation for the observed arithmetic relations.

Lanthanide organic frameworks geometry prediction accuracies of quantum chemical calculations

Semiempirical methods emerge as good candidates for solid-state calculation of molecules with hundreds up to a few thousand atoms, as the use of methods considered more accurate such as DFT demands high computational cost even for molecules with a hundred atoms.In this work, we evaluated how accurately different semiempirical quantum chemical models predict the solid-state geometries of Lanthanide Organic Frameworks (LOFs), comparing the performance of Sparkle/AM1, Sparkle/PM3, Sparkle/PM6, Sparkle/PM7, Sparkle/RM1 and the RM1 methods in the calculation of 83 crystal structures. The geometric parameters chosen were bond lengths and angles, and the accuracy of the models was evaluated based on root mean square deviation (RMSD). Results show that Sparkle/PM3 and Sparkle/RM1 were the most accurate models although all of models evaluated had acceptable accuracies.

Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation.

Most modern semiempirical quantum-chemical (SQC) methods are based on the neglect of diatomic differential overlap (NDDO) approximation to ab initio molecular integrals. Here, we check the validity of this approximation by computing all relevant integrals for 32 typical organic molecules using Gaussian-type orbitals and various basis sets (from valence-only minimal to all-electron triple-ζ basis sets) covering in total more than 15.6 million one-electron (1-e) and 10.3 billion two-electron (2-e) integrals. The integrals are calculated in the nonorthogonal atomic basis and then transformed by symmetric orthogonalization to the Löwdin basis. In the case of the 1-e integrals, we find strong orthogonalization effects that need to be included in SQC models, for example, by strategies such as those adopted in the available OMx methods. For the valence-only minimal basis, we confirm that the 2-e Coulomb integrals in the Löwdin basis are quantitatively close to their counterparts in the atomic basis and that the 2-e exchange integrals can be safely neglected in line with the NDDO approximation. For larger all-electron basis sets, there are strong multishell orthogonalization effects that lead to more irregular patterns in the transformed 2-e integrals and thus cast doubt on the validity of the NDDO approximation for extended basis sets. Focusing on the valence-only minimal basis, we find that some of the NDDO-neglected integrals are reduced but remain sizable after the transformation to the Löwdin basis; this is true for the two-center 2-e hybrid integrals, the three-center 1-e nuclear attraction integrals, and the corresponding three-center 2-e hybrid integrals. We consider a scheme with a valence-only minimal basis that includes such terms as a possible strategy to go beyond the NDDO integral approximation in attempts to improve SQC methods. © 2018 Wiley Periodicals, Inc.

RM1 Semiempirical Quantum Chemistry: Parameters for Trivalent Lanthanum, Cerium and Praseodymium.

The RM1 model for the lanthanides is parameterized for complexes of the trications of lanthanum, cerium, and praseodymium. The semiempirical quantum chemical model core stands for the [Xe]4fn electronic configuration, with n =0,1,2 for La(III), Ce(III), and Pr(III), respectively. In addition, the valence shell is described by three electrons in a set of 5d, 6s, and 6p orbitals. Results indicate that the present model is more accurate than the previous sparkle models, although these are still very good methods provided the ligands only possess oxygen or nitrogen atoms directly coordinated to the lanthanide ion. For all other different types of coordination, the present RM1 model for the lanthanides is much superior and must definitely be used. Overall, the accuracy of the model is of the order of 0.07Å for La(III) and Pr(III), and 0.08Å for Ce(III) for lanthanide-ligand atom distances which lie mostly around the 2.3Å to 2.6Å interval, implying an error around 3% only.

Evaporation of carbon atoms from the open surface of silicon carbide and through graphene cells: Semiempirical quantum-chemical modeling

The evaporation of silicon atoms during the epitaxial growth of graphene on the singular carbon and silicon faces of silicon carbide SiC was modeled by the semiempirical AM1 and PM3 methods. The analysis was performed for evaporation of atoms both from the open surface of SiC and through the surface of the formed graphene monolayers. The total activation barrier of the evaporation of the silicon atoms, their passage from the graphene cell, and further evaporation from graphene was shown to be lower than the barrier to evaporation of the silicon atom on a free surface of SiC. Passage through graphene is thus not the limiting stage of the process, but contributes significantly to the effective evaporation time.

Noncovalent interactions in biochemistry

AbstractNoncovalent interactions are known to play a key role in biochemistry. The knowledge of stabilization (relative) energies and their components is very important for understanding the nature of these interactions. Accurate and benchmark data on interaction (relative) energies and structures can be obtained from coupled‐cluster with single and double and perturbative triple excitations [CCSD(T)] calculations with extended basis of atomic orbitals or even at the complete basis set limit. These methods cannot be, however, used for systems larger than about 50 atoms. In this contribution, the applicability and performance of various recently introduced wavefunction and density functional methods are examined in detail. It is shown that a very good performance by some of these methods is obtained only by introducing empirical parameters fitted mostly to CCSD(T) benchmark data. Among the methods described, special attention is paid to two techniques. First, the symmetry‐adapted perturbation technique that allows obtaining not only accurate values of total interaction energies but also their components. Results of these calculations reveal a key role of dispersion energy in stabilizing the structures of biomolecular systems. Second, the semiempirical quantum chemical parameterized model 6 method (PM6) augmented by empirical terms describing the dispersion and H‐bonding energies. The method is suitable for much extended systems having several thousands of atoms and can be thus used, e.g., in the drug design. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 3‐17 DOI: 10.1002/wcms.8This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics

Synthesis and Spectroscopic Study of Several Novel Annulated Azulene and Azafluoranthene Based Derivatives

A series of cyclized five-membered annulated azafluoranthene (AAF) and seven-membered annulated azulene (AA) derivatives have been synthesized and characterized by spectroscopic methods. The optical absorption and fluorescence spectra have been recorded in organic solvents of different polarity and analyzed within the semiempirical quantum chemical model PM3. In combination with the molecular dynamics simulations it properly reproduces the overall shape of the measured absorption spectra of both AA and AAF dyes including the strongest band in the region of 250-300 nm and the broad first absorption band above 400 nm. While the solvent polarity rises all the dyes exhibit the hypsochromic shift of the first absorption band and the bathochromic shift of the fluorescence band. Such opposite solvatochromic trends appear to be consistent with the Lippert-Mataga solvatochromic model. Compared to AA compounds, both AAF dyes reveal much stronger solvatochromic shift and broadening of the fluorescence band likewise the relative decrease in quantum yield on rising solvent polarity what may be an evidence for the intramolecular charge transfer mechanism being involved into the fluorescence emission. Depending on solvent polarity AA and AAF dyes emit light in the green-yellow range of the visible spectra what may be of interest for potential luminescent or electroluminescent applications.

Lanthanide coordination compounds modeling: Sparkle/PM3 parameters for dysprosium (III), holmium (III) and erbium (III)

The Sparkle model, recently parameterized for all trivalent lanthanide ions using the AM1 semiempirical quantum chemical model, is now parameterized to PM3 method. In a recent paper [R.O. Freire, G.B. Rocha, A.M. Simas, Chem. Phys. Lett. 425 (2006) 138] we defined the Sparkle/PM3 model for Tm(III). Now the Sparkle/PM3 is extend to dysprosium (III), holmium (III) and erbium (III) ions. In the parameterization procedure, we used the same three sets of 15 complexes used to parameterize Sparkle/AM1 for each of these three lanthanide ions, with various representative ligands. The Sparkle/PM3 unsigned mean error, for all interatomic distances between the trivalent lanthanide ion and the ligand atoms of the first sphere of coordination, is 0.072 Å for Dy(III); 0.064 Å for Ho(III); and 0.072 Å for Er(III). These figures are similar to the Sparkle/AM1 ones of 0.066 Å, 0.054 Å, and 0.064 Å, respectively, indicating they are all comparable parameterizations. Moreover, their accuracy is similar to what can be obtained by present-day ab initio effective core potential calculations on such lanthanide complexes. Hence, the choice of which model to use remains with the researcher who must evaluate the impact of either AM1 or PM3 on the quantum chemical description of the organic ligands.

Sparkle/PM3 Parameters for the Modeling of Neodymium(III), Promethium(III), and Samarium(III) Complexes.

The Sparkle/PM3 model is extended to neodymium(III), promethium(III), and samarium(III) complexes. The unsigned mean error, for all Sparkle/PM3 interatomic distances between the trivalent lanthanide ion and the ligand atoms of the first sphere of coordination, is 0.074 Å for Nd(III); 0.057 Å for Pm(III); and 0.075 Å for Sm(III). These figures are similar to the Sparkle/AM1 ones of 0.076 Å, 0.059 Å, and 0.075 Å, respectively, indicating they are all comparable models. Moreover, their accuracy is similar to what can be obtained by present-day ab initio effective potential calculations on such lanthanide complexes. Hence, the choice of which model to utilize will depend on the assessment of the effect of either AM1 or PM3 on the quantum chemical description of the organic ligands. Finally, we present a preliminary attempt to verify the geometry prediction consistency of Sparkle/PM3. Since lanthanide complexes are usually flexible, we randomly generated 200 different input geometries for the samarium complex QIPQOV which were then fully optimized by Sparkle/PM3. A trend appeared in that, on average, the lower the total energy of the local minima found, the lower the unsigned mean errors, and the higher the accuracy of the model. These preliminary results do indicate that attempting to find, with Sparkle/PM3, a global minimum for the geometry of a given complex, with the understanding that it will tend to be closer to the experimental geometry, appears to be warranted. Therefore, the sparkle model is seemingly a trustworthy semiempirical quantum chemical model for the prediction of lanthanide complexes geometries.

Henry’s Law constants or air to water partition coefficients for 1,3,5-triazines by an LFER method

Solvation descriptors have been obtained for 19 substituted 1,3,5-triazines, using literature data on water to solvent partitions, and our own experimental determinations of water to solvent partition coefficients and micellar electrokinetic chromatography (MEKC) retention factors. The solvation descriptors can then be used to predict environmentally important air to water partition coefficients, K(w), which are the reciprocal of Henry's Law constants, with due regard to units. For this class of chemistry it is shown that the values of log K(w) so obtained are generally in good agreement with the experimental values compiled in this work and also compare well with the calculated values from the established bond contribution method of Meylan and Howard as implemented in the EPI Suite, but not with calculated values from the semi-empirical quantum chemical solvation models, SM2 and SM3, recently reported by Delgado and Alderete (J. Chem. Inf. Comput. Sci., 2003, 41, 1226-1230).

Determination of the thermal stability and isothermal bulk modulus of the ZrO 2 polymorphs at room temperature by molecular dynamics with a semi-empirical quantum-chemical model

We evaluated the thermal stability and isothermal bulk modulus of the cubic (c), tetragonal (t), and monoclinic (m) ZrO 2 polymorphs at room temperature by molecular dynamics with a semi-empirical quantum-chemical model. The procedure used was based on the semi-empirical calculation of the lattice energy of the different polymorphs as a function of the lattice volume, followed by fitting the Murnaghan equation of state to these lattice energy–volume curves. This yields directly the equilibrium lattice energy ( E 0), the equilibrium lattice volume ( V 0), and the bulk modulus ( B 0). The monoclinic form ( E 0 m = − 119.41 eV / Zr O 2 ) was found to be more stable than the tetragonal form ( E 0 t = − 119.29 eV / Zr O 2 ), which in turn was more stable than the cubic form ( E 0 c = − 119.21 eV / Zr O 2 ). We thence deduced the existence of the cubic–monoclinic and tetragonal–monoclinic phase transformations, and calculated the volume changes associated with these phase transformations (∼3.9–4.5%) from V 0 c , V 0 t , and V 0 m . Also, we found that the bulk moduli of the ZrO 2 polymorphs are close to 200 GPa, and are in the sequence B 0 t > B 0 c > B 0 m . All these results were in clear agreement with the literature data, obtained by complex ab initio molecular dynamics and/or sophisticated experimental techniques. This suggests that applications of molecular dynamics with semi-empirical quantum-chemical models may have an important role to play in the theoretical design of ceramic materials.

Sparkle model for AM1 calculation of neodymium(III) coordination compounds

The Sparkle/AM1 model, the only available semiempirical quantum chemical model for the calculation of complexes of lanthanide ions, recently defined for Eu(III), Gd(III) and Tb(III), is now extended to Nd(III). Accordingly, all 57 Nd(III) complexes of high crystallographic quality ( R-factor < 0.05 Å), possessing oxygen or nitrogen as directly coordinating atoms, present in the Cambridge Structural Database 2003, were considered. A subset of 15 structures was chosen by cluster analysis to constitute the parameterization training set. All 57 complexes were considered back in the validation part, and the Sparkle/AM1 unsigned mean error, for all interatomic distances between the Nd(III) ion and the ligand atoms of the first sphere of coordination, was found to be 0.07 Å, a level of accuracy useful for luminescent complex design and comparable to present day rare earth complex ab initio/ECP calculations, while being hundreds of times faster.

STM/STS observation of ferrocene derivative adduct to C 60 on HOPG

The C 60ONCFn cycloadduct (Fn=ferrocene) was prepared in the reaction between C 60 and ferrocene oxime, the ferrocene derivative was bound to C 60 at the 6–6 bond by a heterocyclic oxygen–nitrogen–carbon ring; the compound was stable in air. The compound dissolved in dichloroethane was deposited on HOPG and observed by UHV STM/STS methods. The molecules of C 60ONCFn formed several-microns-long straight chains with clearly visible adducted groups pointing to one side of the chain. The STM/STS observations are discussed within the terms of semiempirical quantum chemical molecular modeling.

Carbon-supported palladium catalysts. Molecular orbital study

Geometric and electronic structures of palladium clusters supported on activated carbon (Pd n /AC) are analyzed using semiempirical quantum chemical modeling for n=1–22. Qualitative reliability of the results is checked by DFT calculations for n=1–6. Supported Pd atoms and clusters are shown to be strongly bound to unsaturated and defect surface sites. In such positions, interaction of Pd atoms with the support is much stronger than that with each other. That provides the driving force for atomic dispersity of Pd/AC catalysts. Geometry of small clusters is determined by morphology of an adhesion position. Nanosized particles form compact three-dimensional structures with close-packed triangular surfaces. AC support causes notable excitations in the electronic structure of metal atoms directly bound to the support, resulting in the direct nucleation of fcc-like structures. These excitations are quickly extinguishing when moving far from the support surface.

On the calculation of Henry's law constants of chlorinated benzenes in water from semiempirical quantum chemical methods.

The Henry's law constants for all 12 polychlorinated benzene congeners were calculated using semiempirical quantum chemical solvation models (SM2, SM2.1, and SM3), and their performances are discussed. The values obtained by the SM3 method are underestimated compared with the experimental values and those calculated by SM2 and SM2.1 methods. This underestimation is larger as the degree of chlorination of the benzenes increases. This bad performance of SM3 to calculate Henry's law constants is attributable to the PM3 Hamiltonian, due to its incapacity to give a good description of electron density in chlorinated benzenes. The best results, within the 95% confidence limit of error of the experimental mean, are obtained using SM2 method. The discussion includes analysis of the different contributions to the free energy of solvation, namely, polarization free energy, cavitation, dispersion, and structural rearrangement of the solvent effects as well as partial atomic charges.

Isoresonant Benzenoids

A test is made of the concept of “isoresonance”, wherein two species are so related if each have like numbers of the same (type of) bonds and there is a suitable isomorphism between superpositions of pairs of Kekulé structures. The test is primarily via computations using a few different semiempirical quantum-chemical models on 48 benzenoid structures with over 30 (sometimes overlapping) different isoresonant pairs. Some test is made comparing other experimental data. There is observed to be a high correlation between resonance energies (or certain other properties) of isoresonant pairs-indeed more so than correspondences predicted by some other previously proposed classifications.

Stability of phenol and thiophenol radical cations – interpretation by comparative quantum chemical approaches

The deprotonation kinetics of phenol-type radical cations, formed via a very efficient electron transfer in the pulse radiolysis of non-polar solutions, for example n-chlorobutane, is governed mainly by electronic effects due to the nature of the phenol substituents, whereas steric effects are of minor importance; thiophenols, which are sulphur analogues of phenols, exhibit a similar behavior. Comparative quantum chemical calculations show that the calculated spin densities at the hetero atoms correlate well with the experimentally determined radical cation lifetimes. Not only the Density Functional Theory (DTF) B3LYP but also the semiempirical quantum chemical model PM3 can be applied for the open shell systems mentioned.

Covalent Isoresonance

Two molecular species are defined to be isoresonant if each have like numbers of the same (type of) bonds and there is an isomorphism between superpositions of pairs of Kekulé structures giving equivalent interaction patterns (as appear in Hamiltonian matrices). Thus a close physico-chemical correspondence follows, as predicted by a variety of semiempirical quantum-chemical models, and thence presumably for corresponding molecules. Notably simple structural criteria sufficient for isoresonance are found.