Michael S. Deleuze

A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes.

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of benzene (n=1) and n-acenes (C(4n+2)H(2n+4)) ranging from naphthalene (n=2) to heptacene (n=7) is presented, on the ground of single- and multireference calculations based on restricted or unrestricted zero-order wave functions. High-level and large scale treatments of electronic correlation in the ground state are found to be necessary for compensating giant but unphysical symmetry-breaking effects in unrestricted single-reference treatments. The composition of multiconfigurational wave functions, the topologies of natural orbitals in symmetry-unrestricted CASSCF calculations, the T1 diagnostics of coupled cluster theory, and further energy-based criteria demonstrate that all investigated systems exhibit a (1)A(g) singlet closed-shell electronic ground state. Singlet-triplet (S(0)-T(1)) energy gaps can therefore be very accurately determined by applying the principles of a focal point analysis onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets (X=D, T, Q, 5) and single-reference methods [HF, MP2, MP3, MP4SDQ, CCSD, CCSD(T)] of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations [CCSD(T)] in the limit of an asymptotically complete basis set (cc-pVinfinityZ), the S(0)-T(1) vertical excitation energies of benzene (n=1) and n-acenes (n=2-7) amount to 100.79, 76.28, 56.97, 40.69, 31.51, 22.96, and 18.16 kcal/mol, respectively. Values of 87.02, 62.87, 46.22, 32.23, 24.19, 16.79, and 12.56 kcal/mol are correspondingly obtained at the CCSD(T)/cc-pVinfinityZ level for the S(0)-T(1) adiabatic excitation energies, upon including B3LYP/cc-PVTZ corrections for zero-point vibrational energies. In line with the absence of Peierls distortions, extrapolations of results indicate a vanishingly small S(0)-T(1) energy gap of 0 to approximately 4 kcal/mol (approximately 0.17 eV) in the limit of an infinitely large polyacene.

Valence one-electron and shake-up ionization bands of polycyclic aromatic hydrocarbons. II. Azulene, phenanthrene, pyrene, chrysene, triphenylene, and perylene

An exhaustive investigation of the outer-valence ionization spectra of azulene, phenanthrene, pyrene, chrysene, triphenylene, and perylene is presented. The analysis is based on one-particle Green’s function calculations performed upon correlated [density-functional theory/Becke three-parameter Lee–Yang–Parr (DFT/B3LYP)] geometries using the third-order outer-valence Green’s function [OVGF] and algebraic-diagrammatic construction [ADC(3)] schemes, as well as basis sets of improving quality (6-31G, 6-31G*, cc-pVDZ). The ionization bands of polycyclic aromatic hydrocarbons show a great diversity, which reflects the strong impact of the molecular architecture on orbital energies. Despite the intricacy of ionization spectra and the extent of the shake-up contamination in the π- and σ-band systems, the ADC(3) results enable consistent insights into available ultraviolet photoelectron measurements, up to the inner-valence region. They also indirectly support recent assignments of low-lying π*←π doublet excitati...

High level theoretical study of the structure and rotational barriers of trans-stilbene

The relative energies of stationary points on the potential energy surface of trans-stilbene have been accurately determined using Hartree–Fock, second and third-order Moller–Plesset (MP2, MP3), as well as Coupled Clusters theories with single and double excitations (CCSD), together with a perturbative estimate of connected triple excitations [CCSD(T)], in conjunction with basis sets of increasing size, containing up to 1130 basis functions. A focal point analysis has been carried out in order to determine how the energy differences and rotational barriers approach convergence, enabling extrapolation of the CCSD(T) results to a near-complete basis set. The investigated saddle points pertain to independent rotations of the phenyl rings about the single C–C bond, and to pedalling motions described by a twofold rotation of the central ethylene bond about the longitudinal axis of the molecule. The benchmark calculations presented in this study lead to the conclusion that, in the nonrelativistic limit and with...

Benchmark theoretical study of the ionization threshold of benzene and oligoacenes

In straightforward continuation of Green’s function studies of the ultraviolet photoelectron spectra of polycyclic aromatic compounds [Deleuze et al., J. Chem. Phys. 115, 5859 (2001); M. S. Deleuze, ibid. 116, 7012 (2002)], we present a benchmark theoretical determination of the ionization thresholds of benzene, naphthalene, anthracene, naphthacene (tetracene), pentacene, and hexacene, within chemical accuracy [0.02–0.07 eV]. The vertical ionization potentials of these compounds have been obtained from series of single-point calculations at the Hartree–Fock, second-, third-, and partial fourth-order Moller–Plesset (MP2, MP3, MP4SDQ) levels, and from coupled cluster calculations including single and double excitations (CCSD) as well as a perturbative estimate of connected triple excitations [CCSD(T)], using basis sets of improving quality, introducing up to 510, 790, 1070, 1350, 1630, and 1910 basis functions in the computations, respectively. A focal point analysis of the convergence of the calculated ion...

Focal Point Analysis of the Singlet–Triplet Energy Gap of Octacene and Larger Acenes

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of n-acenes (C(4n+2)H(2n+4)) ranging from octacene (n = 8) to undecacene (n = 11) is presented. The T1 diagnostics of coupled cluster theory and further energy-based criteria demonstrate that all investigated systems exhibit predominantly a (1)A(g) singlet closed-shell electronic ground state. Singlet-triplet (S(0)-T(1)) energy gaps can therefore be very accurately determined by applying the principle of a focal point analysis (FPA) onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets (X = D, T, Q, 5) and single-reference methods [HF, MP2, MP3, MP4SDQ, CCSD, and CCSD(T)] of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations [CCSD(T)] in the limit of an asymptotically complete basis set (cc-pV∞Z), the S(0)-T(1) vertical (adiabatic) excitation energies of these compounds amount to 13.40 (8.21), 10.72 (6.05), 8.05 (3.67), and 7.10 (2.58) kcal/mol, respectively. In line with the absence of Peierls distortions (bond length alternations), extrapolations of results obtained at this level for benzene (n = 1) and all studied n-acenes so far (n = 2-11) indicate a vanishing S(0)-T(1) energy gap, in the limit of an infinitely large polyacene, within an uncertainty of 1.5 kcal/mol (0.06 eV). Lacking experimental values for the S(0)-T(1) energy gaps of n-acenes larger than hexacene, comparison is made with recent optical and electrochemical determinations of the HOMO-LUMO band gap. Further issues such as scalar relativistic, core correlation, and diagonal Born-Oppenheimer corrections (DBOCs) are tentatively examined.

A benchmark theoretical study of the electron affinities of benzene and linear acenes.

A benchmark theoretical determination of the electron affinities of benzene and linear oligoacenes ranging from naphthalene to hexacene is presented, using the principles of a focal point analysis. These energy differences have been obtained from a series of single-point calculations at the Hartree-Fock, second-, third-, and partial fourth-order Moller-Plesset (MP2, MP3, and MP4SDQ) levels and from coupled cluster calculations including single and double excitations (CCSD) as well as perturbative estimates of connected triple excitations [CCSD(T)], using basis sets of improving quality, containing up to 1386, 1350, 1824, 1992, 1630, and 1910 basis functions in the computations, respectively. Studies of the convergence properties of these energy differences as a function of the size of the basis set and order attained in electronic correlation enable a determination of the vertical electron affinities of the four larger terms of the oligoacene (C(2+4n)H(2+2n)) series within chemical accuracy (0.04 eV). According to our best estimates, these amount to +0.28, +0.82, +1.21, and +1.47 eV when n=3, 4, 5, and 6. Adiabatic electron affinities have been further calculated by incorporating corrections for zero-point vibrational energies and for geometrical relaxations. The same procedure was applied to determine the vertical electron affinities of benzene and naphthalene, which are found to be markedly negative ( approximately -1.53 and approximately -0.48 eV, respectively). Highly quantitative insights into experiments employing electron transmission spectroscopy on these compounds were also amenable from such an approach, provided diffuse atomic functions are deliberately removed from the basis set, in order to enforce confinement in the molecular region and enable a determination of pseudoadiabatic electron affinities (with respect to the timescale of nuclear motions). Comparison was made with calculations employing density functional theory and especially designed models that exploit the integer discontinuity in the potential or incorporate a potential wall in the unrestricted Kohn-Sham orbital equation for the anion.

Valence one-electron and shake-up ionization bands of polycyclic aromatic hydrocarbons. I. Benzene, naphthalene, anthracene, naphthacene, and pentacene

The valence ionization bands of benzene and of polyacenes ranging from naphthalene to pentacene have been entirely assigned by means of one-particle Green’s function calculations, performed using the third-order algebraic-diagrammatic construction [ADC(3)] scheme and series of basis sets of improving quality. For the sake of consistency, the computations are based on correlated (DFT/B3LYP) rather than uncorrelated geometries. Ionization bands pertaining to π-orbitals are subject to a severe shake-up contamination at already quite low binding energies (e.g., down to 8.0 eV in the case of pentacene). In sharp contrast, the orbital picture of ionization holds to a much greater extent within the σ-band system (e.g., for pentacene, up to binding energies of 14.6 eV). Despite the intricacy of ionization bands, and, possibly, vibrational complications, ADC(3) spectra consistently match photoionization measurements up to the inner-valence region, where the orbital picture completely breaks down.

Half-metallicity and spin-contamination of the electronic ground state of graphene nanoribbons and related systems: An impossible compromise?

An analysis using the formalism of crystalline orbitals for extended systems with periodicity in one dimension demonstrates that any antiferromagnetic and half-metallic spin-polarization of the edge states in n-acenes, and more generally in zigzag graphene nanoislands and nanoribbons of finite width, would imply a spin contamination S(2) that increases proportionally to system size, in sharp and clear contradiction with the implications of Liebs theorem for compensated bipartite lattices and the expected value for a singlet (S = 0) electronic ground state. Verifications on naphthalene, larger n-acenes (n = 3-10) and rectangular nanographene islands of increasing size, as well as a comparison using unrestricted Hartree-Fock theory along with basis sets of improving quality against various many-body treatments demonstrate altogether that antiferromagnetism and half-metallicity in extended graphene nanoribbons will be quenched by an exact treatment of electron correlation, at the confines of non-relativistic many-body quantum mechanics. Indeed, for singlet states, symmetry-breakings in spin-densities are necessarily the outcome of a too approximate treatment of static and dynamic electron correlation in single-determinantal approaches, such as unrestricted Hartree-Fock or Density Functional Theory. In this context, such as the size-extensive spin-contamination to which it relates, half-metallicity is thus nothing else than a methodological artefact.

Plane wave and orthogonalized plane wave many-body Green's function calculations of photoionization intensities

General equations for the calculation of correlated single-channel photoionization cross-sections of randomly oriented molecules are presented. These equations, employing a plane wave orthogonalized to all (occupied and virtual) bound molecular orbitals as a wavefunction for the photoelectron, are derived in a many-body Greens function framework. Several decoupling approximations for the expansion of the one-particle propagator are then used to compute angle-averaged photoionization cross-sections for a Mg Kα photon source and for a representative set of molecules: CH4, H2O, C2H2, N2, and CO. Both orthogonality corrections to the continuum orbital and many-body corrections in the description of the ionization process are shown to be important for accurate simulations of soft X-ray ionization spectra.

High-level theoretical study of the conformational equilibrium of n-pentane

An accurate calculation of the energy differences between stationary points on the torsional potential energy surface of n-pentane is performed using ab initio Hartree–Fock theory, advanced many-body methods such as MP2, MP3, CCSD, and CCSD(T), as well as density functional theory, together with basis sets of increasing size. This study focuses on the four conformers of this compound, namely, the all staggered trans–trans (TT), trans–gauche (TG), gauche–gauche (G+G+), and gauche–gauche (G+G−) structures, belonging to the C2v, C1, C2, and C1 symmetry point groups, respectively. A focal point analysis up to 635 basis functions is carried out to determine when the series of relative energies of the four conformers approach convergence. It is found that relative to the minimum energy TT conformer, the energy differences of the TG, G+G+, and G+G− conformers obtained from ab initio methods are 0.621, 1.065, and 2.917 kcal mol−1, respectively. Converged energy differences obtained with three density functionals,...