Double Hybrid Functionals and the Π-System Bond Length Alternation Challenge: Rivaling Accuracy of Post-HF Methods

Predicting accurate bond length alternations (BLAs) in long conjugated oligomers has been a significant challenge for electronic-structure methods for many decades, made particularly important by the close relationships between BLA and the rich optoelectronic properties of π-delocalized systems. Here, we test the accuracy of recently developed, and increasingly popular, double hybrid (DH) functionals, positioned at the top of Jacobs Ladder of DFT methods of increasing sophistication, computational cost, and accuracy, due to incorporation of MP2 correlation energy. Our test systems comprise oligomeric series of polyacetylene, polymethineimine, and polysilaacetylene up to six units long. MP2 calculations reveal a pronounced shift in BLAs between the 6-31G(d) basis set used in many studies of BLA to date and the larger cc-pVTZ basis set, but only modest shifts between cc-pVTZ and aug-cc-pVQZ results. We hence perform new reference CCSD(T)/cc-pVTZ calculations for all three series of oligomers against which we assess the performance of several families of DH functionals based on BLYP, PBE, and TPSS, along with lower-rung relatives including global- and range-separated hybrids. Our results show that DH functionals systematically improve the accuracy of BLAs relative to single hybrid functionals. xDH-PBE0 (N4 scaling using SOS-MP2) emerges as a DH functional rivaling the BLA accuracy of SCS-MP2 (N5 scaling), which was found to offer the best compromise between computational cost and accuracy the last time the BLA accuracy of DFT- and wave function-based methods was systematically investigated. Interestingly, xDH-PBE0 (XYG3), which differs to other DHs in that its MP2 term uses PBE0 (B3LYP) orbitals that are not self-consistent with the DH functional, is an outlier of trends of decreasing average BLA errors with increasing fractions of MP2 correlation and HF exchange.

Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van der Waals Corrections

In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems.

Theoretical study of correlated systems using hybrid functionals

Diese Arbeit unterstreicht das Potential von Hybridfunktionalen (B3LYP) für die Untersuchung einer großen Bandbreite von Systemen. Durch die Einbeziehung der exakten Hartree-Fock Austauschenergie kann B3LYP für molekulare und kristalline Systeme eingesetzt werden. Zum Beispiel können stark korrelierte Systeme mit B3LYP erfolgreich erforscht werden. Die elektronische Struktur von PAHs wurde mit B3LYP Hybriddichtefunktionalen untersucht. Mit der ∆SCF-Methode wurden Elektronenbindungsenergien bestimmt, welche die mit UPS gewonnenen experimentellen Resultate bestätigen und ergänzen. Symmetrieeigenschaften der molekularen Orbitale wurden analysiert, um eine Zuordnung und Einschätzung der zugehörigen Signalstärke zu ermöglichen. Während σ-artige Orbitale nur schwer durch UPS-Messungen an dünnen Filmen detektiert werden können, bieten Rechnungen eine detaillierte Einsicht in die verborgenen Teile der Spektren.rnWeiterhin wurden π−π-Komplexe untersucht, welche von verschiedenen Donor- und Akzeptor-Molekülen gebildet werden. Die Moleküle basieren auf polyzyklischen, aromatischen Kohlenwasserstoffen. Für Ladungstransferkomplexe finden DFT Rechnungen ein Minimum in der Oberfläche der potentiellen Energie. Diese attraktive Wechselwirkung wird durch Coulombanziehung verursacht. Allerdings ist die Coulombanziehung nicht die stärkste Wechselwirkung in Ladungstransferkomplexen. Die Einbeziehung von van der Waals-Korrekturen verbessert den intermolekularen Abstand und die Bindungsenergie.rnEine Verkleinerung der intermolekularen Abstände führt zu einer großen Verschiebung der HOMO- und LUMO-Energie.rnAus der Klasse der kristallinen korrelierten Systeme wurden Rb4O6 und FeSe untersucht. Im Falle von Rb4O6 führen Ladungsordnung und Korrelationen zu einem isolierenden Grundzustand. Das hypothetische druckabhängige Phasendiagramm wurde untersucht. Eine Erhöhung des Drucks führt zu einer vergrößerten Bandlücke. Bei etwa 75 GPa wird die Bandbreite W größer als der Bandabstand U und das System nimmt einen homogen gemischt valenten Zustand mit teilweise besetzten π−π-Orbitalen an. Für Drücke ab 160 GPa wird W sehr viel größer als U und das System wird metallisch.rnIm Fall von FeSe finden wir eine korrelierte und isolierende Phase bei hohen Drücken, während das System bei niedrigen Drücken supraleitendes Verhalten zeigt. Die Berechnungen der Elektronenstruktur mit dem Hybridfunktional B3LYP führt zum korrekten halbleitenden Grundzustand in der NiAs- und MnP-Struktur von FeSe. Die Rolle der Korrelationen, der Stöchiometrie und der Nähe zum Magnetismus wird besprochen. Im Speziellen wird gezeigt, dass die Phase mit NiAs-Struktur starke lokale Korrelationen aufweist, was zu einem halbleitenden Zustand in einem weiten Druckbereich führt.

Non-parametrized functionals with empirical dispersion corrections: A happy match?

The performances of two parametrized functionals (namely B3LYP and B2PYLP) have been compared with those of two non-parametrized functionals (PBE0 and PBE0-DH) on a relatively large benchmark set when three different types of dispersion corrections are applied [namely the D2, D3 and D3(BJ) models]. Globally, the MAD computed using non-parametrized functionals decreases when adding dispersion terms although the accuracy not necessarily increases with the complexity of the model of dispersion correction used. In particular, the D2 correction is found to improve the performances of both PBE0 and PBE0-DH, while no systematic improvement is observed going from D2 to D3 or D3(BJ) corrections. Indeed when including dispersion, the number of sets for which PBE0-DH is the best performing functional decreases at the benefit of B2PLYP. Overall, our results clearly show that inclusion of dispersion corrections is more beneficial to parametrized double-hybrid functionals than to non-parametrized ones. The same conclusions globally hold for the corresponding global hybrids, showing that the marriage between non-parametrized functionals and empirical corrections may be a difficult deal.

Theoretical Rationalization of the Singlet–Triplet Gap in OLEDs Materials: Impact of Charge-Transfer Character

New materials for OLED applications with low singlet–triplet energy splitting have been recently synthesized in order to allow for the conversion of triplet into singlet excitons (emitting light) via a Thermally Activated Delayed Fluorescence (TADF) process, which involves excited-states with a non-negligible amount of Charge-Transfer (CT). The accurate modeling of these states with Time-Dependent Density Functional Theory (TD-DFT), the most used method so far because of the favorable trade-off between accuracy and computational cost, is however particularly challenging. We carefully address this issue here by considering materials with small (high) singlet–triplet gap acting as emitter (host) in OLEDs and by comparing the accuracy of TD-DFT and the corresponding Tamm-Dancoff Approximation (TDA), which is found to greatly reduce error bars with respect to experiments thanks to better estimates for the lowest singlet–triplet transition. Finally, we quantitatively correlate the singlet–triplet splitting values with the extent of CT, using for it a simple metric extracted from calculations with double-hybrid functionals, that might be applied in further molecular engineering studies.

Performance of density functionals for calculating barrier heights of chemical reactions relevant to astrophysics

The performance of 39 different LDA, GGA, meta-GGA, and hybrid density functionals has been evaluated, for calculating forward and reverse barrier heights of 10 gas-phase reactions involving hydrogen. The reactions are all relevant to astrochemistry. Special focus is put on the applicability of DFT for calculating the rates of corresponding surface hydrogenation reactions that are relevant to the chemistry of ice-coated interstellar grains. General trends in the performance of the density functionals for reactions involving H atoms, H-2, and OH are discussed. The OH+CO reaction is shown to be a very problematic case for DFT. The best overall performance is found for the hybrid density functionals, such as MPW1K, B97-1, B97-2, and B1B95. For several reactions, the HCTH GGA functionals and the VS98 and OLAP3 meta-GGA functionals also give results that are almost as good as those of the hybrid functionals.

Electronic and magnetic structure of LaMnO3 from hybrid periodic density-functional theory

The electronic and magnetic structures of the LaMnO3 compound have been studied by means of periodic calculations within the framework of spin polarized hybrid density-functional theory. In order to quantify the role of approximations to electronic exchange and correlation three different hybrid functionals have been used which mix nonlocal Fock and local Dirac-Slater exchange. Periodic Hartree-Fock results are also reported for comparative purposes. The A-antiferromagnetic ground state is properly predicted by all methods including Hartree-Fock exchange. In general, the different hybrid methods provide a rather accurate description of the band gap and of the two magnetic coupling constants, strongly suggesting that the corresponding description of the electronic structure is also accurate. An important conclusion emerging from this study is that the nature of the occupied states near the Fermi level is intermediate between the Hartree-Fock and local density approximation descriptions with a comparable participation of both Mn and O states.

Semiconductor-metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides

Using first-principles calculations we show that the band gap of bilayer sheets of semiconducting transition-metal dichalcogenides (TMDs) can be reduced smoothly by applying vertical compressive pressure. These materials undergo a universal reversible semiconductor-to-metal (S-M) transition at a critical pressure. The S-M transition is attributed to lifting of the degeneracy of the bands at the Fermi level caused by interlayer interactions via charge transfer from the metal to the chalcogen. The S-M transition can be reproduced even after incorporating the band gap corrections using hybrid functionals and the GW method. The ability to tune the band gap of TMDs in a controlled fashion over a wide range of energy opens up the possibility for its usage in a range of applications.

Formation energies and the stability of the oxides of K

The most common valencies associated with K and O atoms are 1+ and 2-. As a result, one expects K2O to be the oxide of potassium which is the most stable with respect to its constituents. Calculating the formation energy within electronic structure calculations using hybrid functionals, one finds that K2O2 has the largest formation energy, implying the largest stability of this oxide of potassium with respect to its constituents. This is traced to the presence of oxygen dimers in the K2O2 structure which interact strongly resulting in a larger formation energy compared to the more ionic K2O.

First principles based multiparadigm modeling of electronic structures and dynamics

Electronic structures and dynamics are the key to linking the material composition and structure to functionality and performance.

An essential issue in developing semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band levels. Approximate DFT methods have been justified to predict band gaps from KS/GKS eigenvalues, but the accuracy is decisively dependent on the choice of XC functionals. We show here for CuInSe₂ and CuGaSe₂, the parent compounds of the promising CIGS solar cells, conventional LDA and GGA obtain gaps of 0.0-0.01 and 0.02-0.24 eV (versus experimental values of 1.04 and 1.67 eV), while the historically first global hybrid functional, B3PW91, is surprisingly the best, with band gaps of 1.07 and 1.58 eV. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a MAD of only 0.09 eV, which is substantially better than all modern hybrid functionals, including B3LYP (MAD of 0.19 eV) and screened hybrid functional HSE06 (MAD of 0.18 eV).

The laboratory performance of CIGS solar cells (> 20% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use the B3PW91 hybrid functional of DFT with the AEP method that we validate to provide very accurate descriptions of both band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the CBO of perfect CuInSe₂/CdS interface is large, 0.79 eV, which would dramatically degrade performance. Moreover we show that band gap widening induced by Ga adjusts only the VBO, and we find that Cd impurities do not significantly affect the CBO. Thus we show that Cu vacancies at the interface play the key role in enabling the tunability of CBO. We predict that Na further improves the CBO through electrostatically elevating the valence levels to decrease the CBO, explaining the observed essential role of Na for high performance. Moreover we find that K leads to a dramatic decrease in the CBO to 0.05 eV, much better than Na. We suggest that the efficiency of CIGS devices might be improved substantially by tuning the ratio of Na to K, with the improved phase stability of Na balancing phase instability from K. All these defects reduce interfacial stability slightly, but not significantly.

A number of exotic structures have been formed through high pressure chemistry, but applications have been hindered by difficulties in recovering the high pressure phase to ambient conditions (i.e., one atmosphere and room temperature). Here we use dispersion-corrected DFT (PBE-ulg flavor) to predict that above 60 GPa the most stable form of N₂O (the laughing gas in its molecular form) is a 1D polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03-0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions both polymers relax below 14 GPa to the same stable non-planar trans-polymer, accompanied by possible electronic structure transitions. The predicted phonon spectrum and dissociation kinetics validate the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a new type of conducting polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions.

Modeling non-adiabatic electron dynamics has been a long-standing challenge for computational chemistry and materials science, and the eFF method presents a cost-efficient alternative. However, due to the deficiency of FSG representation, eFF is limited to low-Z elements with electrons of predominant s-character. To overcome this, we introduce a formal set of ECP extensions that enable accurate description of p-block elements. The extensions consist of a model representing the core electrons with the nucleus as a single pseudo particle represented by FSG, interacting with valence electrons through ECPs. We demonstrate and validate the ECP extensions for complex bonding structures, geometries, and energetics of systems with p-block character (C, O, Al, Si) and apply them to study materials under extreme mechanical loading conditions.

Despite its success, the eFF framework has some limitations, originated from both the design of Pauli potentials and the FSG representation. To overcome these, we develop a new framework of two-level hierarchy that is a more rigorous and accurate successor to the eFF method. The fundamental level, GHA-QM, is based on a new set of Pauli potentials that renders exact QM level of accuracy for any FSG represented electron systems. To achieve this, we start with using exactly derived energy expressions for the same spin electron pair, and fitting a simple functional form, inspired by DFT, against open singlet electron pair curves (H₂ systems). Symmetric and asymmetric scaling factors are then introduced at this level to recover the QM total energies of multiple electron pair systems from the sum of local interactions. To complement the imperfect FSG representation, the AMPERE extension is implemented, and aims at embedding the interactions associated with both the cusp condition and explicit nodal structures. The whole GHA-QM+AMPERE framework is tested on H element, and the preliminary results are promising.

Produtividade de híbridos de milho em função da velocidade de semeadura

O presente trabalho foi conduzido na área experimental do Laboratório de Máquinas e Mecanização Agrícola da UNESP - Jaboticabal, em um Latossolo Vermelho eutroférrico, em preparo convencional. Avaliaram-se o desenvolvimento e os componentes de produção de dois híbridos de milho (DKB 390, simples e DKB 435, duplo) em função de três velocidades do conjunto trator-semeadora-adubadora (5,4; 6,8 e 9,8 km h-1), totalizando seis tratamentos, com quatro repetições, em delineamento em blocos ao acaso, em esquema fatorial 2 x 3. Os resultados evidenciaram que o aumento da velocidade do conjunto trator-semeadora-adubadora reduziu a produtividade de grãos para o híbrido simples e não interferiu na produtividade do híbrido duplo. Apenas na menor velocidade (5,4 km h-1), o híbrido simples apresentou maior produtividade de grãos, comparado com o híbrido duplo. O aumento da velocidade na operação de semeadura reduziu a percentagem de espaçamentos normais entre as sementes, independentemente do híbrido estudado.

Produção de forragem verde em sistema hidropônico usando esgoto tratado

In the urban areas of the cities a larger problem of destiny of effluents of the treatment stations is verified due to the junction of the sewages in great volumes. This way the hidroponic cultive becomes important, for your intensive characteristic, as alternative of reuse. This work presents as objective the improvement of the relation hidric-nutritious of the hidroponic cultive of green forage (FVH) using treaty sewage. The production of forage was with corn (Zea mays L.), using double hybrid AG1051, in the experimental field of the Federal University of Rio Grande do Norte (UFRN), in the city of Natal-RN-Brazil. The treated effluent essentially domestic had origin of anaerobic reactor, type decant-digester of two cameras in series followed by anaerobic filters drowned. The hidroponic experimental system was composed of 08 stonemasons, with limited contours for masonry of drained ceramic brick, measuring each one 2,5 meters in length for 1,0 meter of width, with inclination of 4% (m/m) in the longitudinal sense, leveled carefully, in way to not to allow preferential roads in the flow. These dimensions, the useful area of Isow was of 2 square meters. The stonemasons of cultive were waterproof (found and lateral) with plastic canvas of 200 micres of thickness, in the white color. Controlled the entrance and exit of the effluente in the stonemasons, with cycles of 12,68 minutes, it being water of 1,18 minutes. The treatments were constituted of: T1 - 24 hours/day under it waters with flow of 2 L/min; T2 - 12 hours/day under waters with flow of 4 L/min; T3 - 12 hours/day under waters with flow of 2 L/min; and T4 - 16 hours/day under waters with flow of 3 L/min. There were evaluations of the evapotranspirometric demand, of hidroponic system affluent and effluent seeking to characterize and to monitor physical-chemical parameters as: pH, temperature, Electric Conductivity and Fecal Coliforms. This last one was analyzed to the 11 days after isow (DAS) and to the 14 DAS. The others were analyzed daily. I sow it was accomplished in the dates of February 21, 2007, first experiment, and April 10, 2007, second experiment. The density of Isow was of 2 kg of seeds, germinated before 48 hours, for square meter of stonemason. The statistic delineament was it casual entirely with two repetitions, in two experiments. It was applied Tukey test of average to five percent of probability. The cultivation cycle was of 14 DAS with evapotranspirometric demand maximum, reached by T1, of 67,44 mm/day. The analyzed parameters, as mass of green matter - Kg, productivity-Kg/m2 and reason of production of seed FVH/Kg used in Isow, the best result was presented by T1, obtaining value of up to 19,01 Kg/m2 of cultive. Without significant difference, the T4 presented greats values with 16 hours under cycle of water. The Treatments 2 and 3 with 12 hours under cycle of water, they obtained inferior results to the other Treatments. As treatment system, came efficient in the reduction of the salinity. T1 obtained reduction medium maxim of 62,5%, to the 7 DAS, in the amount of salts that enter in the system in they are absorbed in the cultivation. The cultivation FVH acted reducing the microbiologic load. Significant percentile of reduction they were reached, with up to 90,23% of reduction of Units of Colonies (UFC), constituting, like this, the Hidroponic System as good alternative of treatment of effluents of Reactors of high Efficiency

Efeitos de doses não equidistantes de N, P, K nas concentrações destes macronutrientes na folha e na produção do milho (Zea mays L.)

Os experimentos foram conduzidos, em um podzólico de Lins e Marília - variação Lins, de textora barrento-arenosa, localizado no Município de Monte Azul Paulista, SP. O híbrido de milho duplo H-6999B foi utilizado. Cada experimento constou de 5 tratamentos e de 4 repetições. Os níveis de nitrogênio foram: 0, 50, 100, 200 e 400 kg/ha, sendo aplicados também90 kg/ha de P²O5 e 50 kg/ha de K2O. Os níveis de fósforo foram: 0,40, 80, I60 e 320 kg/ha de P²O5, sendo aplicados também 100 kg/ha de N e 50 kg/ha de K2O. Os níveis de potássio foram: 0, 25, 50, 100 e 200 kg/ha de K2O, sendo aplicados também 100 kg/ha de N e 90 kg/ha de P²O5. A aplicação tanto das doses de fósforo comodas de nitrogênio fez aumentar a produção de milho, a qual foi da ordem de 3 a 7 vezes superior à média de produção do Estado de São Paulo. A dose econômica e a sua consequente produção, determinadas pelas equações de Mitscherlichr-Pimentel Gomes foram: para o fósforo, de 253 kg/ha de P²O5 correspondente a urna produção de o.877 kg/ha de milho em grão; para o nitrogênio, foi de 228 kg/ha de N correspondente a uma produção de 11.100 kg/ha de milho e para o potássio, foi de 62 kg/ha de K2O correspondente a urna produção de 9-252 kg/ha de milho. Os níveis críticos econômicos, nas folhas, determinados pelas equações de MALAVOLTA & PIMENTEL GOMES (1961) e correspondentes às doses econômicas, foram de: 0,293% de P, de 3,27% de N e de 2,07% de K. A folha escolhida, ou seja, aquela oposta à espiga mais alta, reflete bem o estado nutricional da planta e consequentemente o nível de fertilidade do solo.

Custo de produção e indicadores de rentabilidade da cultura do milho safrinha

The objective of this study was to evaluate the production cost and profitability of the second season corn crop in the Medio Paranapanema region, São Paulo State Brazil, under two technological levels (middle and high technology), crop 2008/2009, and compare the results with the 2006/2007 agricultural year. Effective and total operational cost as well as five profitability indicators were used. It was concluded that the high technology production cost for corn crop (direct seedling, sowing during the recommended period, use of simple hybrid seed, application of side-dressing fertilization, and treatment of seeds with different insecticides) was superior to the middle technology production cost (direct seedling, sowing after the recommended time, use of double hybrid seed, and no side-dressing fertilization). However, the average cost was inferior (US$ 8.5), due to a higher yield (4 t). The high technology corn crop was profitable (gross income and profitability index of 14% and 12%, respectively). For the middle technology crop, profitability indexes pointed out that the cropping system needs to be reevaluated by technicians and research institutions, regarding the adequate technical recommendations. Profitability indexes decreased considerably in both cropping systems. It was verified that, in relation to the 2006/2007 harvest period, the total operational cost increased for both technologies, mainly because of the increase of supplies prices.

Produtividade e perdas na colheita de dois cultivares híbridos de milho em função da velocidade de semeadura

Pós-graduação em Agronomia (Ciência do Solo) - FCAV