The ab initio density functional theory applied for spin-polarized calculations.

We have performed a systematic and broad study of the performance of the ab initio OEP2-sc functional for spin-polarized systems, including the computation of ionization potentials and atomization and reaction energies of closed- and open-shell molecules. The results have revealed that, in line with other second-order methods, OEP2-sc can provide accurate results, being competitive to the orbital-optimized MP2 method. Moreover, the analysis of total and relative energies has shown that, unlike the case of double-hybrid functionals, this relatively good performance is not based on an error cancellation effect.

Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method.

We extend the range-separated double-hybrid RSH+MP2 method (Ángyán, J. G.; et al. Phys. Rev. A 2005, 72, 012510), combining long-range HF exchange and MP2 correlation with a short-range density functional to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter µ = 0.5 bohr-1, we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.

Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation.

We have studied the correlation potentials produced by various adiabatic connection models (ACMs) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-interaction limit potentials have also been investigated and discussed.

Spin-Component-Scaled ΔMP2 Parametrization: Toward a Simple and Reliable Method for Ionization Energies.

A practical, accurate, and cost- and implementation-free method (ΔMP2-SOS(IP)) for the calculation of vertical ionization potentials is proposed. The simple method is based on a single-step, a diagonal, frequency-independent approximation to the second-order self-energy expression combined with the spin-component-scaled technique. The search for an optimal scaling factor is performed for a set of 50 moderately sized molecules, and the quality of the method is additionally assessed for a benchmark set of 24 organic acceptor molecules. The proposed ΔMP2-SOS(IP) method provides the best results of valence ionization energies as compared to the several standard self-consistent variants of the electron propagator methods at the second and higher orders (EP2, SCS-EP2, EP3, OVGF) with almost CCSD(T) or IP-EOM-CCSD accuracy and the cost of only a single opposite-spin ΔMP2-type calculation ( O( N3)). For core ionization energies, our new methods outperform the standard ΔMP2 results due to a better balanced treatment of the correlation and relaxation term in the second-order self-energy.

Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method.

We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Møller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules. While the OEP-based self-consistency does not provide any improvement for the calculations of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities.

Accurate Kohn-Sham ionization potentials from scaled-opposite-spin second-order optimized effective potential methods.

One important property of Kohn-Sham (KS) density functional theory is the exact equality of the energy of the highest occupied KS orbital (HOMO) with the negative ionization potential of the system. This exact feature is out of reach for standard density-dependent semilocal functionals. Conversely, accurate results can be obtained using orbital-dependent functionals in the optimized effective potential (OEP) approach. In this article, we investigate the performance, in this context, of some advanced OEP methods, with special emphasis on the recently proposed scaled-opposite-spin OEP functional. Moreover, we analyze the impact of the so-called HOMO condition on the final quality of the HOMO energy. Results are compared to reference data obtained at the CCSD(T) level of theory. © 2016 Wiley Periodicals, Inc.

Detection of discoloration in diesel fuel based on gas chromatographic fingerprints.

In the countries of the European Community, diesel fuel samples are spiked with Solvent Yellow 124 and either Solvent Red 19 or Solvent Red 164. Their presence at a given concentration indicates the specific tax rate and determines the usage of fuel. The removal of these so-called excise duty components, which is known as fuel "laundering", is an illegal action that causes a substantial loss in a government's budget. The aim of our study was to prove that genuine diesel fuel samples and their counterfeit variants (obtained from a simulated sorption process) can be differentiated by using their gas chromatographic fingerprints that are registered with a flame ionization detector. To achieve this aim, a discriminant partial least squares analysis, PLS-DA, for the genuine and counterfeit oil fingerprints after a baseline correction and the alignment of peaks was constructed and validated. Uninformative variables elimination (UVE), variable importance in projection (VIP), and selectivity ratio (SR), which were coupled with a bootstrap procedure, were adapted in PLS-DA in order to limit the possibility of model overfitting. Several major chemical components within the regions that are relevant to the discriminant problem were suggested as being the most influential. We also found that the bootstrap variants of UVE-PLS-DA and SR-PLS-DA have excellent predictive abilities for a limited number of gas chromatographic features, 14 and 16, respectively. This conclusion was also supported by the unitary values that were obtained for the area under the receiver operating curve (AUC) independently for the model and test sets.

Orbital-dependent second-order scaled-opposite-spin correlation functionals in the optimized effective potential method.

The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analysed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn-Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite-spin OEP functional [I. Grabowski, E. Fabiano, and F. Della Sala, Phys. Rev. B 87, 075103 (2013)] which is the most advantageous from a computational point of view. We find that for high accuracy, a careful, system dependent, selection of the scaling coefficient is required. We analyse several size-extensive approaches for this selection. Finally, we find that a composite approach, named OEP2-SOSh, based on a post-SCF rescaling of the correlation energy can yield high accuracy for many properties, being comparable with the most accurate OEP procedures previously reported in the literature but at substantially reduced computational effort.

A simple non-empirical procedure for spin-component-scaled MP2 methods applied to the calculation of the dissociation energy curve of noncovalently-interacting systems.

We present a simple and non-empirical method to determine optimal scaling coefficients, within the (spin-component)-scaled MP2 approach, for calculating intermolecular potential energies of noncovalently-interacting systems. The method is based on an observed proportionality between (spin-component) MP2 and CCSD(T) energies for a wide range of intermolecular distances and allows us to compute with high accuracy a large portion of the dissociation curve at the cost of a single CCSD(T) calculation. The accuracy of the present procedure is assessed for a series of noncovalently-interacting test systems: the obtained results reproduce CCSD(T) quality in all cases and definitely outperform conventional MP2, CCSD and SCS-MP2 results. The difficult case of the beryllium dimer is also considered.

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential.

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order Møller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.

Ab initio density functional theory applied to quasidegenerate problems.

Ab initio density functional theory (DFT), previously applied primarily at the second-order many-body perturbation theory (MBPT) level, is generalized to selected infinite-order effects by using a new coupled-cluster perturbation theory (CCPT). This is accomplished by redefining the unperturbed Hamiltonian in ab initio DFT to correspond to the CCPT2 orbital dependent functional. These methods are applied to the Be-isoelectronic systems as an example of a quasidegenerate system. The CCPT2 variant shows better convergence to the exact quantum Monte Carlo correlation potential for Be than any prior attempt. When using MBPT2, the semicanonical choice of unperturbed Hamiltonian, plays a critical role in determining the quality of the obtained correlation potentials and obtaining convergence, while the usual Kohn-Sham choice invariably diverges. However, without the additional infinite-order effects, introduced by CCPT2, the final potentials and energies are not sufficiently accurate. The issue of the effects of the single excitations on the divergence in ordinary OEP2 is addressed, and it is shown that, whereas their individual values are small, their infinite-order summation is essential to the good convergence of ab initio DFT.

The exchange-correlation potential in ab initio density functional theory.

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.