We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom–atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

/pdf/long-range-corrected-hybrid-density-functionals-with-damped-44ti6za9f3.pdf

Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections

Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections Jeng-Da Chai ∗ and Martin Head-Gordon † Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (Dated: June 14, 2008) We report re-optimization of a recently proposed long-range corrected (LC) hybrid density func- tionals [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent sys- tems, ωB97X-D shows slight improvement over other empirical dispersion-corrected density func- tionals, while for covalent systems and kinetics, it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is signiﬁcantly superior for non-bonded interactions, and very similar in performance for bonded interactions. I. INTRODUCTION Due to its favorable cost-to-performance ratio, Kohn- Sham density-functional theory (KS-DFT) [1, 2] has be- come the most popular electronic structure theory for large-scale ground-state systems [3–5]. Its extension for treating excited-state systems [6, 7], time-dependent den- sity functional theory (TDDFT), has also been developed to the stage where it is now very widely used. The essential ingredient of KS-DFT, the exchange- correlation energy functional E xc , remains unknown and needs to be approximated. Semi-local gradient-corrected density functionals, though successful in many applica- tions, lead to qualitative failures in some circumstances, where the accurate treatment of non-locality of exchange- correlation hole becomes crucial. These situations occur mostly in the asymptotic regions of molecular systems, such as spurious self-interaction eﬀects upon dissociation [8, 9] and dramatic failures for long-range charge-transfer excitations [10–12]. Widely used hybrid density function- als, like B3LYP [13, 14], do not qualitatively resolve these problems. These self-interaction errors can be qualitatively re- solved using the long-range corrected (LC) hybrid density functionals [15, 16, 18], which employ 100% Hartree-Fock (HF) exchange for long-range electron-electron interac- tions. This is accomplished by a partition of unity, using erf(ωr)/r for long-range (treated by HF exchange) and erfc(ωr)/r for short-range (treated by an exchange func- tional), with the parameter ω controlling the partition- ing. Over the past ﬁve years, the LC hybrid scheme has been attracting increasing attention [15] since its compu- tational cost is comparable with standard hybrid func- tionals [13]. However, LC functionals have tended to be inferior to the best hybrids for properties such as ther- mochemistry. ∗ Electronic † Author address: jdchai@berkeley.edu to whom correspondence should be addressed. Electronic address: mhg@cchem.berkeley.edu Recently we have improved the overall accuracy at- tainable with the LC functionals by using a systematic optimization procedure [18]. One important conclusion is that optimizing LC and hybrid functionals with identical numbers of parameters in their GGA exchange and cor- relation terms leads to noticeably better results for all properties using the LC form. The resulting LC func- tional is called ωB97. Further statistically signiﬁcant improvement results from re-optimizing the entire func- tional with one extra parameter corresponding to an ad- justable fraction of short-range exact exchange, deﬁning the ωB97X functional. Independent test sets covering thermochemistry and non-covalent interactions support these conclusions. However, problems associated with the lack of non-locality of the correlation hole, such as the lack of dispersion interactions (London forces), still remain, as the semi-local correlation functionals cannot capture long-range correlation eﬀects [19, 20]. There have been signiﬁcant eﬀorts to develop a frame- work that can account for long-range dispersion eﬀects within DFT. Zaremba and Kohn (ZK) [21] derived an exact expression for the second-order dispersion energy in terms of the exact density-density response functions of the two separate systems. To obtain a tractable non- local dispersion functional, Dobson and Dinite (DD) [22] made local density approximations to the ZK response functions. DD’s non-local correlation functional was ob- tained independently [23] by modifying the eﬀective den- sity deﬁned in the earlier work of Rapcewicz and Ashcroft Starting from the formally exact expression of KS- DFT, the adiabatic connection ﬂuctuation-dissipation theorem (ACFDT), for the ground-state exchange- correlation energy, Langreth and co-workers [25] devel- oped a so-called van der Waals density functional (vdW- DF) by making a series of reasonable approximations to yield a computationally tractable scheme. Recently, Becke and Johnson (BJ) developed a series of post-HF correlation models with a novel treatment for dispersion interactions based on the exchange-hole dipole moment [26]. The origin of dispersion claimed in the BJ models was recently questioned by Alonso, and A.

Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Large polycyclic aromatic hydrocarbon (PAH) molecules carry the infrared (IR) emission features that dominate the spectra of most galactic and extragalactic sources. This review surveys the observed mid-IR characteristics of these emission features and summarizes laboratory and theoretical studies of the spectral characteristics of PAHs and the derived intrinsic properties of emitting interstellar PAHs. Dedicated experimental studies have provided critical input for detailed astronomical models that probe the origin and evolution of interstellar PAHs and their role in the universe. The physics and chemistry of PAHs are discussed, emphasizing the contribution of these species to the photoelectric heating and the ionization balance of the interstellar gas and to the formation of small hydrocarbon radicals and carbon chains. Together, these studies demonstrate that PAHs are abundant, ubiquitous, and a dominant force in the interstellar medium of galaxies.

Interstellar Polycyclic Aromatic Hydrocarbon Molecules

We present a quantitative model for the infrared emission from dust in the diffuse interstellar medium. The model consists of a mixture of amorphous silicate grains and carbonaceous grains, each with a wide size distribution ranging from molecules containing tens of atoms to large grains 1 μm in diameter. We assume that the carbonaceous grains have properties like polycyclic aromatic hydrocarbons (PAHs) at very small sizes and graphitic properties for radii a 50 A. On the basis of recent laboratory studies and guided by astronomical observations, we propose astronomical absorption cross sections for use in modeling neutral and ionized PAHs from the far-ultraviolet to the far-infrared. We also propose modifications to the far-infrared emissivity of astronomical silicate. We calculate energy distribution functions for small grains undergoing temperature spikes caused by stochastic absorption of starlight photons using realistic heat capacities and optical properties. Using a grain-size distribution consistent with the observed interstellar extinction, we are able to reproduce the near-IR to submillimeter emission spectrum of the diffuse interstellar medium, including the PAH emission features at 3.3, 6.2, 7.7, 8.6, and 11.3 μm. The model is compared with the observed emission at high Galactic latitudes as well as in the Galactic plane, as measured by the COBE/DIRBE, COBE/FIRAS, IRTS/MIRS, and IRTS/NIRS instruments. The model has 60 × 10-6 of C (relative to H) locked up in PAHs, with 45 × 10-6 of C in a component peaking at ~6 A (NC ≈ 100 carbon atoms) to account for the PAH emission features and with 15 × 10-6 of C in a component peaking at ~50 A to account for the 60 μm flux. The total infrared emission is in excellent agreement with COBE/DIRBE observations at high Galactic latitudes, just as the albedo for our grain model is in accord with observations of the diffuse Galactic light. The aromatic absorption features at 3.3 and 6.2 μm predicted by our dust model are consistent with observations. We calculate infrared emission spectra for our dust model heated by a range of starlight intensities, from 0.3 to 104 times the local interstellar radiation field, and we tabulate the intensities integrated over the SIRTF/IRAC and MIPS bands. We also provide dust opacities tabulated from the extreme-ultraviolet to submillimeter wavelengths.

https://iopscience.iop.org/article/10.1086/323147/pdf

Infrared Emission from Interstellar Dust. II. The Diffuse Interstellar Medium

The IR vibrational and visible/UV electronic absorption spectra of the anthracene cation, An(+), were studied experimentally, in argon matrices at 12 K, as well as theoretically, using ab initio calculations for the vibrational modes and enhanced semiempirical methods with configuration interaction for the electronic spectra. It was found that both approaches predicted well the observed photoelectron spectrum. The theoretical IR intensities showed some remarkable differences between neutral and ionized species (for example, the CH in-plane bending modes and CC in-plane stretching vibrations were predicted to increase by several orders of magnitude upon ionization). Likewise, estimated experimental IR intensities showed a significant increase in the cation band intensities over the neutrals. The implication of these findings for the hypothesis that polycyclic aromatic hydrocarbon cations are responsible for the unidentified IR emission bands from interstellar space is discussed.

Electronic and vibrational spectra of matrix isolated anthracene radical cations - Experimental and theoretical aspects

In order to test the hypothesis of ionized PAHs as possible carriers of the UIR bands, we realized a computational exploration on selected PAHs of small dimension in order to identify which changes ionization would induce on their IR spectra. In this study we performed ab initio calculations of the spectra of neutral and positively ionized naphthalene, anthracene, and pyrene. The results are significantly important. The frequencies in the cations are slightly shifted with respect to the neutral species, but no general conclusion can be reached from the three molecules considered. By contrast, the relative intensities of most vibrations are strongly affected by ionization, leading to a much better agreement between the calculated CH/CC vibration intensity ratios and those deduced from observations.

Theoretical infrared spectra of some model polycyclic aromatic hydrocarbons: effect of ionization.

Context. Pure gas-phase chemistry models do not succeed in reproducing the measured abundances of small hydrocarbons in the interstellar medium. Information on key gas-phase progenitors of these molecules sheds light on this problem. Aims: We aim to constrain the chemical content of the Horsehead mane with a millimeter unbiased line survey at two positions, namely the photo-dissociation region (PDR) and the nearby shielded core. This project revealed a consistent set of eight unidentified lines toward the PDR position. We associate them to the l-C3H+ hydrocarbon cation, which enables us to constrain the chemistry of small hydrocarbons. We observed the lowest detectable J line in the millimeter domain along a cut toward the illuminating direction to constrain the spatial distribution of the l-C3H+ emission perpendicular to the photo-dissociation front. Methods: We simultaneously fit 1) the rotational and centrifugal distortion constants of a linear rotor; and 2) the Gaussian line shapes located at the eight predicted frequencies. A rotational diagram is then used to infer the excitation temperature and the column density. We finally compare the abundance to the results of the Meudon PDR photochemical model. Results: Six out of the eight unidentified lines observable in the millimeter bands are detected with a signal-to-noise ratio from 6 to 19 toward the Horsehead PDR, while the two last ones are tentatively detected. Mostly noise appears at the same frequency toward the dense core, located less than 40'' away. Moreover, the spatial distribution of the species integrated emission has a shape similar to radical species such as HCO, and small hydrocarbons such as C2H, which show enhanced abundances toward the PDR. The observed lines can be accurately fitted with a linear rotor model, implying a 1Σ ground electronic state. The deduced rotational constant value is B = 11 244.9512 ± 0.0015 MHz, close to that of l-C3H. Conclusions: This is the first detection of the l-C3H+ hydrocarbon in the interstellar medium. Laboratory spectroscopy is underway to confirm these results. Interferometric imaging is needed to firmly constrain the small hydrocarbon chemistry in the Horsehead. Based on observations obtained with the IRAM-30 m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain).

/pdf/the-iram-30-m-line-survey-of-the-horsehead-pdr-ii-first-vbn6139ua7.pdf

The IRAM-30 m line survey of the Horsehead PDR - II. First detection of the l-C3H+ hydrocarbon cation

Electronic and Vibrational Spectra Of Matrix-Isolated Pyrene Radical Cations: Theoretical and Experimental Aspects

We present the first detection of the l-C3H+ hydrocarbon in the interstellar medium. The Horsehead WHISPER project, a millimeter unbiased line survey at two positions, namely the photo-dissociation region (PDR) and the nearby shielded core, revealed a consistent set of eight unidentified lines toward the PDR position. Six of them are detected with a signal-to-noise ratio from 6 to 19, while the two last ones are tentatively detected. Mostly noise appears at the same frequency toward the dense core, located less than 40" away. We simultaneously fit 1) the rotational and centrifugal distortion constants of a linear rotor, and 2) the Gaussian line shapes located at the eight predicted frequencies. The observed lines can be accurately fitted with a linear rotor model, implying a 1Sigma ground electronic state. The deduced rotational constant value is Be= 11244.9512 +/- 0.0015 MHz, close to that of l-C3H. We thus associate the lines to the l-C3H+ hydrocarbon cation, which enables us to constrain the chemistry of small hydrocarbons. A rotational diagram is then used to infer the excitation temperature and the column density. We finally compare the abundance to the results of the Meudon PDR photochemical model.

/pdf/the-iram-30m-line-survey-of-the-horsehead-pdr-ii-first-rl43895q9u.pdf

Dahbia Talbi

Papers

Electronic and vibrational spectra of matrix isolated anthracene radical cations - Experimental and theoretical aspects

Theoretical infrared spectra of some model polycyclic aromatic hydrocarbons: effect of ionization.

The IRAM-30 m line survey of the Horsehead PDR - II. First detection of the l-C3H+ hydrocarbon cation

Electronic and Vibrational Spectra Of Matrix-Isolated Pyrene Radical Cations: Theoretical and Experimental Aspects

The IRAM-30m line survey of the Horsehead PDR: II. First detection of the l-C3H+ hydrocarbon cation