Alfredo M. Simas

RM1: A reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I

Twenty years ago, the landmark AM1 was introduced, and has since had an increasingly wide following among chemists due to its consistently good results and time‐tested reliability—being presently available in countless computational quantum chemistry programs. However, semiempirical molecular orbital models still are of limited accuracy and need to be improved if the full potential of new linear scaling techniques, such as MOZYME and LocalSCF, is to be realized. Accordingly, in this article we present RM1 (Recife Model 1): a reparameterization of AM1. As before, the properties used in the parameterization procedure were: heats of formation, dipole moments, ionization potentials and geometric variables (bond lengths and angles). Considering that the vast majority of molecules of importance to life can be assembled by using only six elements: C, H, N, O, P, and S, and that by adding the halogens we can now build most molecules of importance to pharmaceutical research, our training set consisted of 1736 molecules, representative of organic and biochemistry, containing C, H, N, O, P, S, F, Cl, Br, and I atoms. Unlike AM1, and similar to PM3, all RM1 parameters have been optimized. For enthalpies of formation, dipole moments, ionization potentials, and interatomic distances, the average errors in RM1, for the 1736 molecules, are less than those for AM1, PM3, and PM5. Indeed, the average errors in kcal · mol−1 of the enthalpies of formation for AM1, PM3, and PM5 are 11.15, 7.98, and 6.03, whereas for RM1 this value is 5.77. The errors, in Debye, of the dipole moments for AM1, PM3, PM5, and RM1 are, respectively, 0.37, 0.38, 0.50, and 0.34. Likewise, the respective errors for the ionization potentials, in eV, are 0.60, 0.55, 0.48, and 0.45, and the respective errors, in angstroms, for the interatomic distances are 0.036, 0.029, 0.037, and 0.027. The RM1 average error in bond angles of 6.82° is only slightly higher than the AM1 figure of 5.88°, and both are much smaller than the PM3 and PM5 figures of 6.98° and 9.83°, respectively. Moreover, a known error in PM3 nitrogen charges is corrected in RM1. Therefore, RM1 represents an improvement over AM1 and its similar successor PM3, and is probably very competitive with PM5, which is a somewhat different model, and not fully disclosed. RM1 possesses the same analytical construct and the same number of parameters for each atom as AM1, and, therefore, can be easily implemented in any software that already has AM1, not requiring any change in any line of code, with the sole exception of the values of the parameters themselves.

The Laplacian of the charge density and its relationship to the shell structure of atoms and ions

The Laplacian of the spherically averaged charge density ∇2ρ(r) has been computed from nonrelativistic SCF wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium, in order to examine the shell structure. ∇2ρ(r) exhibits a number of extremal points and zeros with the absolute value of the function becoming smaller at each successive extremal point. The zeros, in particular the odd numbered zeros, are shown to exhibit good correlation with the Bohr theory of an atom while the extremal points correlate to a lesser extent. At most five shells are seen in the studied atomic cases based on the fact that the odd numbered zeros are the topological feature of ∇2ρ(r) most indicative of a shell.

Sparkle model for the quantum chemical AM1 calculation of europium complexes

Abstract Considering that the bonds between a lanthanide and its ligands essentially possess an electrostatic character, we propose the representation of rare-earth elements within AM1 as sparkles. To parametrize the sparkle model we have used the known geometry of the complex tris (acetylacetonate) (1,10-phenantroline) of europium (III). Interatomic distances for the coordination polyhedron, averaging 2.81 A, could be predicted with an average deviation of 0.13 A. In short, this is a simple lanthanide-ligand electrostatic model which simultaneously treats the organic ligands and their interactions with the powerful AM1 method, yielding results of useful accuracy.

Sparkle/PM6 Parameters for all Lanthanide Trications from La(III) to Lu(III)

PM6 is the first semiempirical method to be released already parametrized for the elements of the periodic table, from hydrogen to bismuth (Z = 83), with the exception of the lanthanides from cerium (Z = 58) to ytterbium (Z = 70). In order to fill this gap, we present in this article a generalization of our Sparkle Model for the quantum chemical semiempirical calculation of lanthanide complexes to PM6. Accordingly, we present Sparkle/PM6 parameters for all lanthanide trications from La(III) to Lu(III). The validation procedure again considered only high-quality crystallographic structures and included 633 complexes. Sparkle/PM6 unsigned mean errors UME(Ln-L)s, corresponding to all the interatomic distances between the lanthanide ion and the atoms directly coordinated to it, range from 0.066 to 0.086 Å for Gd(III) and Ce(III), respectively. These minimum and maximum UME(Ln-L)s across the lanthanide series are comparable to the Sparkle/AM1 values of 0.054 and 0.085 Å for Ho(III) and Pr(III), respectively, as well as to the values for Sparkle/PM3 of 0.064 and 0.093 Å for Gd(III) and Pr(III), respectively. Moreover, for all 15 lanthanide ions, these interatomic distance deviations follow a γ distribution within a 95% level of confidence, indicating that these errors appear to be random around a mean, freeing the model of systematic errors, at least within the validation set. Sparkle/PM6 presented here, therefore, broadens the range of applicability of PM6 to the coordination compounds of the rare earth metals.

Internally folded densities

The 3q-dimensional Fourier transforms of the q-electron charge density and momentum density respectively are defined to be the q-electron form factor and internally folded density. For q = 1, these quantities are just the usual X-ray form factor and the B(r) function recently introduced for the analysis of Compton profiles. Numerous properties of the one-electron internally folded density B(r) are derived. B(r) functions for the atoms from He through Ne are calculated and examined for chemical content with the help of the concept of reduced Compton profiles.

THEORETICAL MODEL FOR THE PREDICTION OF ELECTRONIC SPECTRA OF LANTHANIDE COMPLEXES

A technique is introduced for the theoretical prediction of electronic spectra of lanthanide complexes by replacing the metal ion by a point charge with the ligands held in their positions as determined by the SMLC/AM1, and by computing the theoretical spectra via the intermediate neglect of differential overlap/spectroscopic-configuration interaction (INDO/S-CI). As a test case, we report the absorption spectrum of tris(picolinate-N-oxide)(2,2′: 6′,2″-terpyridine) of EuIII complex which has been synthesized in our laboratory. The predicted absorption spectra (complex and free ligands) compare well with the UV region experimental data. Moreover, the computed triplet energy levels display transitions near 470 and 560 nm which are due to the N-oxide and which may be relevant for the luminescence.

Sparkle/PM3 for the modeling of europium(III), gadolinium(III), and terbium(III) complexes

O modelo Sparkle/PM3 e parametrizado para complexos de europio (III), gadolinio (III) e terbio (III). A validacao do modelo foi realizada utilizando noventa e seis complexos de Eu(III), setenta complexos de Gd(III) e quarenta e dois complexos de Tb(III); todos a partir de estruturas cristalograficas de alta qualidade, com fator R < 5%. Os erros medios absolutos, obtidos com o modelo Sparkle/PM3, considerando todas as distâncias interatomicas do tipo lantanideo-atomo ligante, foram 0,080 A para Eu(III), 0,063 A para Gd(III) e 0,070 A para Tb(III). Estes valores medios sao similares aos obtidos com o modelo Sparkle/AM1 (0,082 A, 0,061 A, e 0,068 A, respectivamente). Alem disso, a exatidao em reproduzir o poliedro de coordenacao de complexos de Eu(III), Gd(III) e Tb(III) e similar a obtida utilizando metodos ab initio com potenciais efetivos de caroco. Finalmente, com o objetivo de avaliar se as geometrias preditas com o modelo Sparkle/PM3 sao confiaveis, escolhemos um dos complexos de Eu(III), BAFZEO, para o qual geramos centenas de diferentes geometrias iniciais, onde variamos de forma aleatoria as distâncias e ângulos entre os ligantes e o ion Eu(III). Em seguida, todas essas geometrias iniciais foram otimizadas usando o modelo Sparkle/PM3. Como resultado, observamos uma tendencia significativa onde a geometria que apresentou o menor erro medio absoluto apresentou tambem a energia total mais baixa, o que reforca a validade do modelo Sparkle. The Sparkle/PM3 model is extended to europium(III), gadolinium(III), and terbium(III) complexes. The validation procedure was carried out using only high quality crystallographic structures, for a total of ninety-six Eu(III) complexes, seventy Gd(III) complexes, and forty-two Tb(III) complexes. 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: 0.080 A for Eu(III); 0.063 A for Gd(III); and 0.070 A for Tb(III). These figures are similar to the Sparkle/AM1 ones of 0.082 A, 0.061 A, and 0.068 A 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 full geometry optimization calculations on such lanthanide complexes. Finally, we report a preliminary attempt to show that Sparkle/PM3 geometry predictions are reliable. For one of the Eu(III) complexes, BAFZEO, we created hundreds of different input geometries by randomly varying the distances and angles of the ligands to the central Eu(III) ion, which were all subsequently fully optimized. A significant trend was unveiled, indicating that more accurate local minima geometries cluster at lower total energies, thus reinforcing the validity of sparkle model calculations.

A Comprehensive Strategy to Boost the Quantum Yield of Luminescence of Europium Complexes

Lanthanide luminescence has many important applications in anion sensing, protein recognition, nanosized phosphorescent devices, optoelectronic devices, immunoassays, etc. Luminescent europium complexes, in particular, act as light conversion molecular devices by absorbing ultraviolet (UV) light and by emitting light in the red visible spectral region. The quantum yield of luminescence is defined as the ratio of the number of photons emitted over the number of UV photons absorbed. The higher the quantum yield of luminescence, the higher the sensitivity of the application. Here we advance a conjecture that allows the design of europium complexes with higher values of quantum yields by simply increasing the diversity of good ligands coordinated to the lanthanide ion. Indeed, for the studied cases, the percent boost obtained on the quantum yield proved to be strong: of up to 81%, accompanied by faster radiative rate constants, since the emission becomes less forbidden.

Mesoionic rings as efficient asymmetric bridges for the design of compounds with large optical nonlinearities

Abstract Through semi-empirical AM1 calculations of second-order nonlinear optical properties of molecules containing mesoionic rings, we propose that these should be considered as promising substitutes for the polyene bridges normally present in compounds displaying large hyperpolarizabilities, β. In order to substantiate our reasoning, we computed the AM1 static hyperpolarizabilities, β(0), of twenty molecules whose experimental values have already been determined. Our results indicate that the AM1 β(0) are indeed able to yield qualitative inferences about experimentally obtained values. Finally, we present a number of theoretically designed molecular structures which should display high hyperpolarizability values.

On the applicability of CNDO indices for the prediction of chemical reactivity

A series of CNDO/2 molecular orbital properties were evaluated to determine their utility in parameterizing chemical reactivities. Some of these indices were used previously for only Π electron methods and were extended here to include the σ framework. Theoretical rationales were given for this extension to the semi-empirical all valence electron methods. Four systems, the aromatic hydrocarbons, the benzene derivatives, the substituted benzoic acids, and the substituted phenyl amines, were studied to test how well these indices can parameterize chemical reactivities. This study focused on reactions involving both σ and π electrons where the reactive site is not necessarily on the aromatic framework. For the nonplanar and heteropolar systems, these indices performed as well as the Hückel method did for the classical aromatics. These CNDO indices should perform effectively in multivariable regressions to parameterize the reactivities for more complicated problems such as those encountered in quantitative structure activity relationships of drugs.