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.

Systematic Improvement of Density Functionals through Parameter-Free Hybridization Schemes

It is suggested here that the ultimate accuracy of DFT methods arises from the type of hybridization scheme followed. This idea can be cast into a mathematical formulation utilizing an integrand connecting the noninteracting and the interacting particle system. We consider two previously developed models for it, dubbed as HYB0 and QIDH, and assess a large number of exchange-correlation functionals against the AE6, G2/148, and S22 reference data sets. An interesting consequence of these hybridization schemes is that the error bars, including the standard deviation, are found to markedly decrease with respect to the density-based (nonhybrid) case. This improvement is substantially better than variations due to the underlying density functional used. We thus finally hypothesize about the universal character of the HYB0 and QIDH models.

Some applications of logic to feasibility in higher types

While it is commonly accepted that computability on a Turing machine in polynomial time represents a correct formalization of the notion of a feasibly computable function, there is no similar agreement on how to extend this notion on functionals, that is, what functionals should be considered feasible. One possible paradigm was introduced by Mehlhorn, who extended Cobham's definition of feasible functions to type 2 functionals. Subsequently, this class of functionals (with inessential changes of the definition) was studied by Townsend who calls this class POLY, and by Kapron and Cook who call the same class basic feasible functionals. Kapron and Cook gave an oracle Turing machine model characterisation of this class. In this article, we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalise the corresponding properties of the class of feasible functions, thus giving further evidence that the notion of feasibility of functionals mentioned above is correctly chosen. We also improve the Kapron and Cook result on machine representation.Our proofs are based on essential applications of logic. We introduce a weak fragment of second order arithmetic with second order variables ranging over functions from NN which suitably characterises basic feasible functionals, and show that it is a useful tool for investigating the properties of basic feasible functionals. In particular, we provide an example how one can extract feasible programs from mathematical proofs that use nonfeasible functions.

A density functional theory study of CO2 and N2 adsorption on aluminium nitride single walled nanotubes

Strong binding of isolated carbon dioxide (CO2) on aluminium nitride (AlN) single walled nanotubes is verified using two different functionals. Two optimized configurations corresponding to physisorption and chemisorption are linked by a low energy barrier, such that the chemisorbed state is accessible and thermodynamically favored at low temperatures. In contrast, N2 is found only to form a physisorbed complex with the AlN nanotube, suggesting the potential application of aluminium nitride based materials for CO2 fixation. The effect of nanotube diameter on gas adsorption properties is also discussed. The diameter is found to have an important effect on the chemisorption of CO2, but has little effect on the physisorption of either CO2 or N2.

Direct Observation of Photodissociation Products from Phenylperoxyl Radicals Isolated in the Gas Phase

Gas phase peroxyl radicals are central to our chemical understanding of combustion and atmospheric processes and are typically characterized by strong absorption in the UV (lambda(max) approximate to 240 nm). The analogous maximum absorption feature for arylperoxyl radicals is predicted to shift to the visible but has not previously been characterized nor have any photoproducts arising from this transition been identified. Here we describe the controlled synthesis and isolation in vacuo of an array of charge-substituted phenylperoxyl radicals at room temperature, including the 4-(N,N,N-trimethylammonium)methyl phenylperoxyl radical cation (4-Me3N[+]CH2-C6H4OO center dot), using linear ion-trap mass spectrometry. Photodissociation mass spectra obtained at wavelengths ranging from 310 to 500 nm reveal two major photoproduct channels corresponding to homolysis of aryl-OO and arylO-O bonds resulting in loss of O-2 and O, respectively. Combining the photodissociation yields across this spectral window produces a broad (FWHM approximate to 60 nm) but clearly resolved feature centered at lambda(max) = 403 nm (3.08 eV). The influence of the charge-tag identity and its proximity to the radical site are investigated and demonstrate no effect on the identity of the two dominant photoproduct channels. Electronic structure calculations have located the vertical (B) over tilde <- (X) over tilde transition of these substituted phenylperoxyl radicals within the experimental uncertainty and further predict the analogous transition for unsubstituted phenylperoxyl radical (C6H5OO center dot) to be 457 nm (2.71 eV), nearly 45 nm shorter than previous estimates and in good agreement with recent computational values.

Interface of graphane with copper : a van der Waals density-functional study

Various forms of hydrogenated graphene have been produced to date by several groups, while the synthesis of pure graphane has not been achieved yet. The study of the interface between graphane, in all its possible hydrogenation configurations, and catalyst metal surfaces can be pivotal to assess the feasibility of direct CVD growth methods for this material. We investigated the adhesion of graphane to a Cu(111) surface by adopting the vdW-DF2-C09 exchange-correlation functional, which is able to describe dispersion forces. The results are further compared with the PBE and the LDA exchange-correlation functionals. We calculated the most stable geometrical configurations of the slab/graphane interface and evaluated how graphane's geometrical parameters are modified. We show that dispersion forces play an important role in the slab/graphane adhesion. Band structure calculations demonstrated that in the presence of the interaction with copper, the band gap of graphane is not only preserved, but also enlarged, and this increase can be attributed to the electronic charge accumulated at the interface. We calculated a substantial energy barrier at the interface, suggesting that CVD graphane films might act as reliable and stable insulating thin coatings, or also be used to form compound layers in conjunction with metals and semiconductors.

On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.

Quantum Chemical Studies on Tropospheric Nucleation Mechanisms Involving Sulfuric Acid

Nucleation is the first step of the process by which gas molecules in the atmosphere condense to form liquid or solid particles. Despite the importance of atmospheric new-particle formation for both climate and health-related issues, little information exists on its precise molecular-level mechanisms. In this thesis, potential nucleation mechanisms involving sulfuric acid together with either water and ammonia or reactive biogenic molecules are studied using quantum chemical methods. Quantum chemistry calculations are based on the numerical solution of Schrödinger's equation for a system of atoms and electrons subject to various sets of approximations, the precise details of which give rise to a large number of model chemistries. A comparison of several different model chemistries indicates that the computational method must be chosen with care if accurate results for sulfuric acid - water - ammonia clusters are desired. Specifically, binding energies are incorrectly predicted by some popular density functionals, and vibrational anharmonicity must be accounted for if quantitatively reliable formation free energies are desired. The calculations reported in this thesis show that a combination of different high-level energy corrections and advanced thermochemical analysis can quantitatively replicate experimental results concerning the hydration of sulfuric acid. The role of ammonia in sulfuric acid - water nucleation was revealed by a series of calculations on molecular clusters of increasing size with respect to all three co-ordinates; sulfuric acid, water and ammonia. As indicated by experimental measurements, ammonia significantly assists the growth of clusters in the sulfuric acid - co-ordinate. The calculations presented in this thesis predict that in atmospheric conditions, this effect becomes important as the number of acid molecules increases from two to three. On the other hand, small molecular clusters are unlikely to contain more than one ammonia molecule per sulfuric acid. This implies that the average NH3:H2SO4 mole ratio of small molecular clusters in atmospheric conditions is likely to be between 1:3 and 1:1. Calculations on charged clusters confirm the experimental result that the HSO4- ion is much more strongly hydrated than neutral sulfuric acid. Preliminary calculations on HSO4- NH3 clusters indicate that ammonia is likely to play at most a minor role in ion-induced nucleation in the sulfuric acid - water system. Calculations of thermodynamic and kinetic parameters for the reaction of stabilized Criegee Intermediates with sulfuric acid demonstrate that quantum chemistry is a powerful tool for investigating chemically complicated nucleation mechanisms. The calculations indicate that if the biogenic Criegee Intermediates have sufficiently long lifetimes in atmospheric conditions, the studied reaction may be an important source of nucleation precursors.

A functional style of programming with CSP-like communication mechanisms

This paper introduces CSP-like communication mechanisms into Backus’ Functional Programming (FP) systems extended by nondeterministic constructs. Several new functionals are used to describe nondeterminism and communication in programs. The functionals union and restriction are introduced into FP systems to develop a simple algebra of programs with nondeterminism. The behaviour of other functionals proposed in this paper are characterized by the properties of union and restriction. The axiomatic semantics of communication constructs are presented. Examples show that it is possible to reason about a communicating program by first transforming it into a non-communicating program by using the axioms of communication, and then reasoning about the resulting non-communicating version of the program. It is also shown that communicating programs can be developed from non-communicating programs given as specifications by using a transformational approach.

Limit Laws for Coverage in Backbone-Sensor Networks

We study the coverage in sensor networks having two types of nodes, sensor and backbone nodes. Each sensor is capable of transmitting information over relatively small distances. The backbone nodes collect information from the sensors. This information is processed and communicated over an ad-hoc network formed by the backbone nodes,which are capable of transmitting over much larger distances. We consider two modes of deployment of sensors, one a Poisson-Poisson cluster model and the other a dependently-thinned Poisson point process. We deduce limit laws for functionals of vacancy in both models using properties of association for random measures.

Study on the structure and vibrational spectra of efavirenz conformers using DFT: Comparison to experimental data

Efavirenz, (S)-6-chloro-4-(cyclopropylethynyl)-1,4-dihydro-4-(trifluoromethyl)-2H-3 ,1-benzoxazin-2-one, is an anti HIV agent belonging to the class of the non-nucleoside inhibitors of the HIV-1 virus reverse transcriptase. A systematic quantum chemical study of the possible conformations, their relative stabilities and vibrational spectra of efavirenz has been reported. Structural and spectral characteristics of efavirenz have been studied by vibrational spectroscopy and quantum chemical methods. Density functional theory (DFT) calculations for potential energy curve, optimized geometries and vibrational spectra have been carried out using 6-311++G(d,p) basis sets and B3LYP functionals. Based on these results, we have discussed the correlation between the vibrational modes and the crystalline structure of the most stable form of efavirenz. A complete analysis of the experimental infrared and Raman spectra has been reported on the basis of wavenumber of the vibrational bands and potential energy distribution. The infrared and the Raman spectra of the molecule based on OFT calculations show reasonable agreement with the experimental results. The calculated HOMO and LUMO energies shows that charge transfer occur within the molecule. (C) 2011 Elsevier B.V. All rights reserved.

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.

DFT study of structure and vibrational spectra of ceramide 3: comparison to experimental data

The Fourier transform Raman and infrared (IR) spectra of the Ceramide 3 (CER3) have been recorded in the regions 200-3500 cm(-1) and 680-4000 cm(-1), respectively. We have calculated the equilibrium geometry, harmonic vibrational wavenumbers, electrostatic potential surfaces, absolute Raman scattering activities and IR absorption intensities by the density functional theory with B3LYP functionals having extended basis set 6-311G. This work is undertaken to study the vibrational spectra of CER3 completely and to identify the various normal modes with better wavenumber accuracy. Good consistency is found between the calculated results and experimental data for the IR and Raman spectra.

Limit laws for coverage in backbone-sensor networks

We study coverage in sensor networks having two types of nodes, namely, sensor nodes and backbone nodes. Each sensor is capable of transmitting information over relatively small distances. The backbone nodes collect information from the sensors. This information is processed and communicated over an ad hoc network formed by the backbone nodes, which are capable of transmitting over much larger distances. We consider two models of deployment for the sensor and backbone nodes. One is a PoissonPoisson cluster model and the other a dependently thinned Poisson point process. We deduce limit laws for functionals of vacancy in both models using properties of association for random measures.