1Ag States Research Articles

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited 1Δg state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for 1La and 1Lb states in polyacenes and 1Au and 1Ag states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

Taming the excited states of butadiene, hexatriene, and octatetraene using state specific multireference perturbation theory with density functional theory orbitals.

To compute the electronic excitation energies, a state-specific multireference Møller-Plesset perturbation theory (SSMRPT) with a complete active space configuration interaction reference function constructed using the orbitals obtained by the density functional theory (DFT) is presented as an accurate, as well as computationally affordable, and efficient protocol at the level of second order. The global hybrid B3LYP (Becke, 3-parameter, Lee-Yang-Parr) functional has been used to generate orbitals. The present method, called DFT-SSMRPT, uses perturbers that are individual Slater determinants and accounts for the coupling between the nondynamical and dynamical correlation effects. We have applied the new method to compute excitation energies in conjugated systems of π-electrons such as trans-1,3-butadiene, trans,trans-1,3,5-hexatriene, and all-trans-1,3,5,7-octatetraene. The ordering of the excited states is correctly reproduced by the DFT-SSMRPT calculations. The relative ordering of low-lying excited 1Bu and 1Ag states alters when the length of the polyene changes. The results match reasonably well with the literature including experimental and best theoretical findings. The accuracy of the method is sufficient to discern the energy gap between the close low-lying singlet and triplet states. The DFT-SSMRPT appears as an affordable computational ab initio avenue for a qualitatively correct description of excitation energies.

Polyacetylene: Myth and Reality.

Polyacetylene, the simplest and oldest of potentially conducting polymers, has never been made in a form that permits rigorous determination of its structure. Trans polyacetylene in its fully extended form will have a potential energy surface with two equivalent minima. It has been assumed that this results in bond length alternation. It is, rather, very likely that the zero-point energy is above the Peierls barrier. The experimental studies that purport to show bond alternation are reviewed and shown to be compromised by serious experimental inconsistencies or by the presence, for which there is considerable evidence, of finite chain polyenes. In this view, addition of dopants results in conductivity by facilitation of charge transport between finite polyenes. The double minimum potential that necessarily occurs for polyacetylene, if viewed as the result of elongation of finite chains, originates from admixture of the 11Ag ground electronic state with the 21Ag excited electronic singlet state. This excitation is diradical (two electron) in character. The polyacetylene limit is an equal admixture of these two 1Ag states making theory intractable for long chains. A method is outlined for preparation of high molecular weight polyacetylene with fully extended chains that are prevented from reacting with neighboring chains.

Theoretical Design of a Molecular Switch with Controlled Hydrogen Bonds: Electronic and Vibrational Spectra of [Co(2,2′-biimidazole)(C6H4O2)(NH3)2

Abstract The electronic and vibrational spectra of a proton–electron-coupled inorganic complex [Co(Hbim)(C6H4O2)(NH3)2]2 having multistable states, were theoretically investigated using density functional theory calculations using B3LYP parameters. The electronic excitation spectrum in the low-spin ground 1Ag state of the complex has no strong absorption in the visible region (600–700 nm), while in the high-spin 5A1 and 9Ag complexes, some prominent peaks were predicted in the visible region. Frequency analyses of the 1Ag, 5A1, and 9Ag states showed the strong band of the NH stretching vibration at 2690, 2120, and 2770 cm−1, respectively. Based on this, it is possible to distinguish 5A1 from 1Ag and 9Ag by measuring IR light absorption at 2120 cm−1, showing that [Co(Hbim)(C6H4O2)(NH3)2]2 would be a good candidate for use as optically durable molecular level memory.

Theoretical Study of Rhenium Dinuclear Complexes: Re−Re Bonding Nature and Electronic Structure

Four dinuclear rhenium complexes, [Re2Cl8](2-) (1), [Re2(mu-Cl)3Cl6](2-) (2a), [Re2(mu-Cl)3Cl6](-) (2b), and [Re2(mu-Cl)2Cl8](2-) (3), were theoretically investigated by the CASSCF, MRMP2, SA-CASSCF, and MCQDPT methods. Interesting differences in electronic structure and Re-Re bonding nature among these complexes are clearly reported here, as follows: In 1, the ground state is the 1A1g state. The approximate stabilization energies by the sigma, pi, and delta bonding interactions are evaluated to be 4.36, 2.89, and 0.52 eV, respectively, by the MRMP2 method. In 2a, the ground state is the 2E" state. The approximate stabilization energy by two degenerate delta bonding interactions is estimated to be 0.36 eV by the MCQDPT method. One delta bonding interaction of 2a is much weaker than that of 1, which is discussed in terms of the Re-Re distance and the Re oxidation state. In 2b, the ground state is the 1A1' state, of which multiconfigurational nature is extremely large unlike that of the 2E" ground state of 2a despite similarities between 2a and 2b. In 3, the sigma, pi, and delta bonding interactions are not effectively formed between two Re centers. As a result, the 1Ag, 3B1u, 5Ag, and 7B1u states are in almost the same energy within 0.03 eV. This result is consistent with the paramagnetism of 3 experimentally reported.

The third-order polarizability γ of C60: The role of low-lying two-electron excited singlet states Ag and Hg

The third-order polarizability γ of the C60 molecule has been calculated for the third harmonic generation at several incident frequencies using two different schemes of the sum-over-state (SOS) method, and the contribution of the low-lying singlet excited states as the second intermediate states has been analyzed. The group-theoretical analysis of the SOS expression clarifies that the 1Ag and 1Hg states are the only states that contribute to the γ as the second intermediate states. For the numerical analysis, the electronic states previously obtained in the semiempirical CNDO/S approximation with the singly and doubly excited configuration interaction method are used. It is found that the inclusion of the doubly excited configurations is essential in evaluating the γ. Those excited 1Ag and 1Hg states which make significant positive contributions to the γ are practically the doubly excited states. In order to secure error-free SOS calculations, equivalent but independent calculations have been also carried out with the frequency-dependent moment method.

Spectroscopic Properties of Al2P2, Al2P2+, and Al2P2- and Comparison with Their Ga and In Analogues

Sixteen electronic states of Al2P2, three states of Al2P2+, and the ground state of Al2P2- are studied using the complete active-space MCSCF (CASSCF) followed by multireference singles + doubles configuration interaction (MRSDCI). The 1Ag, 2B1u, and 2B1g electronic states with rhombus equilibrium structures were found to be the ground states of Al2P2, Al2P2+, and Al2P2-, respectively. Alternative structures such as T-shaped, linear, and trapezoidal structures were considered, but the equilibrium geometry of the ground state was found to be the rhombus structure. Our computed results are compared with anion photoelectron spectroscopic studies of Neumark and co-workers. Comparison of electronic states of M2P2 (M = Al, Ga, and In) was made. It is shown that the electronic states of In2P2 exhibit anomalies due to relativistic effects.

On the Electronic Nature of a Butadienyl Biradical – Experiments and ab initio MO Calculations

The spin state of the biradical obtained upon heating 1,6-diisopropyl-1,6-diazacyclodeca-3,8-diyne (9b) has been investigated. 9b was heated in biphenyl, naphthalene, and bromobenzene at 150 °C in the presence of a mixture of [D4]- and [D0]-9,10-dihydroanthracene (DHA) as hydrogen source. The relative contributions of the cage (C) and cage-escape (E) reaction paths could be determined by analysing the products 2,6-diisopropyl-1,2,3,5,6,7-hexahydro-2,6-naphthy-ridine (11b) and 2,6-diisopropyl-4-(9,10-dihydroanthra-cenyl)-1,2,3,5,6,7-hexahydro-2,6-naphthyridine (12b) and their deuterated analogues. The C/E ratio could be determined by GC-MS analysis and was found to be 0.30 in biphenyl, 0.40 in naphthalene, and 0.22 in bromobenzene, and to be more or less independent of the DHA concentration over a wide range. The energetics of the cyclization of 1,6-diazacyclodeca-3,8-diyne (9a) to 1,2,3,5,6,7-hexahydro-2,6-naphthyridine-2,6-diyl (10b) have been investigated at several levels of theory. Calculations of the various structures along the reaction coordinate at the CASPT2/6-31G* level yield an energy difference of 10.7 kcal/mol between 9a and 10a and of 17.8 kcal/mol between 9a and the transition state (14a). The transition state shows only weak biradical character, indicating that the electronic structure of 9a is retained as long as possible. The energy difference between the 1Ag and 3Au states of 10a is predicted to be 13.0 kcal/mol.

Octatetraene m 1A g states: Two-photon fluorescence excitation spectrum from 28 000 to 50 000 cm−1

The 2-photon fluorescence excitation spectra of all-trans octatetraene in n-hexane and n-octane host crystals at 77 and 1.8 K have been recorded for the region 28 000 to 50 000 cm−1. Measurements of the dependence of emission signal on excitation intensity and fluorescence lifetimes contributed to the assignment of the observed features. On the basis of their frequencies, intensities, and solvent shift behaviors all of the bands are seen in the region 28 000 to 44 000 cm−1 are assigned to vibronic bands of the 1 1Ag–2 1Ag transition. The unusual temperature dependence of one excitation feature is consistent with a near degeneracy of singlet and triplet levels. Above 44 000 cm−1 there are four broadbands, two of which must be assigned to 0–0 transitions from the 1 1Ag ground state to higher lying m 1Ag states at 45 030 and 46 710 cm−1, respectively. The other two bands at 48 000 and 49 860 cm−1 could be either vibronic additions to the 0–0 band at 46 710 cm−1 or 0–0 bands for new m 1Ag states.

The 2 1A g state of trans,trans-1,3,5,7-octatetraene in free jet expansions

One- and two-photon fluorescence excitation and emission spectra of the S1↔S0 transition of trans,trans-1,3,5,7-octatetraene have been measured for the first time in free jet expansions. The one-photon excitation spectrum is the same, with the exception of significant differences in the intensities of a few lines, as the two-color, resonance-enhanced, two-photon ionization spectrum, previously assigned to the 2 1A′←1 1A′ transition of cis,trans-1,3,5,7-octatetraene. However, comparison of the one- and two-photon fluorescence excitation spectra shows clearly that the carrier of the spectrum has inversion symmetry, as expected for trans,trans-1,3,5,7-octatetraene. The one-photon spectrum is built on bu Herzberg–Teller promoting modes, which are origins of progressions in ag modes, while the two-photon spectrum is due to a single progression in ag modes starting from the 2 1Ag←1 1Ag electronic origin. The appearance of out-of-plane vibrations, possibly including torsions of the polyene framework, suggests large differences in force constants and perhaps in the geometries of the 2 1Ag and 1 1Ag potential surfaces. For 2 1Ag vibronic levels with energies ≤1000 cm−1, the fluorescence lifetimes vary between 170 and 450 ns due to the dependence of radiative and nonradiative decay rates on the vibronic state. An abrupt increase in the nonradiative decay rates at ∼2100 cm−1 excess energy is tentatively ascribed to trans→cis isomerization. This work demonstrates that the one- and two-photon cross sections of the 2 1Ag←1 1Ag transitions of all-trans linear polyenes are sufficiently large to allow the study of 2 1Ag states under isolated, unperturbed conditions.

Electronic structure of group IV tetramers (Si4–Pb4)

Geometries and energy separations of ten electronic states of Ge4, Sn4, and Pb4 are computed and compared with Si4. We employ complete active space multiconfiguration self-consistent-field followed by multireference singles + doubles configuration interaction calculations. The ground states of Ge4–Pb4 are found to be 1Ag states with equilibrium geometries of rhombus similar to Si4. Relativistic effects are found to be significant for Pb4. Atomization/dissociation energies of Ge4–Pb4 are computed and compared with Si4. Pb4 was found to be considerably less bound compared to other tetramers. The energy separations of the excited electronic states were found to decrease, especially the splitting between the rhombus and tetrahedral structures, as one goes down the group.

Excitation shifts of parallel conjugated polymers due to π-electron dispersion forces

Molecular exciton methods are extended to obtain excited-state shifts of parallel conjugated strands arising from interchain Coulomb interactions. A method is developed to evaluate second-order corrections involving π-electron dispersion forces, with exact Pariser–Parr–Pople states of isolated segments as zeroth-order functions. Crystal shifts are estimated for polyacetylene (PA) at interchain separation d=3.9 Å; the two-photon excitation to the covalent 2 1Ag state is hardly shifted, but the one-photon excitation to 1 1Bu is red shifted by ∼0.30 eV and specific higher n 1Ag states are strongly red shifted by ∼1 eV. Their stabilization correlates with charge separation and ionicity in the excited state. Excitation shifts due to π-electron dispersion forces do not parallel changes in the static polarizability and show unusual long-range behavior of d−3 in the interchain separation.

ChemInform Abstract: Ab initio Study of the Two‐Photon Bound‐Bound Electronic Transitions of trans‐Butadiene.

The two‐photon absorption properties of trans‐1,3‐butadiene have been calculated at an ab initio level employing RPA vertical excitation energies and transition moments and taking the random molecular orientation into account. For single‐beam two‐photon absorption with every possible combination of photon polarization the transition probability coefficients and polarization ratios for the low‐lying 1Ag and 1Bg final states are reported. The strongest two‐photon absorptivity is predicted under excitation from linearly polarized photons for 1Ag states and from circularly polarized photons for 1Bg states. The polarization ratios take sizably different values for the various 1Ag states. The case of concerted absorption of two photons with various polarizations from two laser beams has also been investigated exhaustively as a function of the photon frequencies.

Geometry relaxation effects in the 1 1Bu and 2 1Ag states of trans-1,3-butadiene

MCSCF and MRCI calculations on the first three singlet states of trans-1,3-butadiene are presented. Flexible basis sets were applied and full geometry optimization was carried out at the MCSCF level for planar and selected non-planar structures including twisting and pyramidalization of terminal CH2-groups. Geometry relaxations in and excitation energies to 1 1Bu and 2 1Ag states are discussed in detail. For planar structures the covalent 2 1Ag state is lower in energy than the 1 1Bu state. If non-planar geometry relaxations are allowed, the lowest lying non-planar excited singlet state turns out to be ionic with one terminal CH2 group rotated by 90°. Limitations of the current investigations due to restrictions in the MRCI treatment and because of incomplete scanning of excited state surfaces are pointed out.

A b i n i t i o study of the two-photon bound–bound electronic transitions of t r a n s-butadiene

The two-photon absorption properties of trans-1,3-butadiene have been calculated at an ab initio level employing RPA vertical excitation energies and transition moments and taking the random molecular orientation into account. For single-beam two-photon absorption with every possible combination of photon polarization the transition probability coefficients and polarization ratios for the low-lying 1Ag and 1Bg final states are reported. The strongest two-photon absorptivity is predicted under excitation from linearly polarized photons for 1Ag states and from circularly polarized photons for 1Bg states. The polarization ratios take sizably different values for the various 1Ag states. The case of concerted absorption of two photons with various polarizations from two laser beams has also been investigated exhaustively as a function of the photon frequencies.

ChemInform Abstract: FREE‐JET FLUORESCENCE EXCITATION SPECTRUM OF TRANS,TRANS‐1,3,5,7‐OCTATETRAENE

The fluorescence excitation spectrum from 2980 to 2650 A of trans, trans‐1,3,5,7‐octatetraene in a free jet has been measured monitoring emission in the region 3250 to 3500 A. The vibronic bands of the 1 1Bu←1 1Ag (S2←S0) transition of octatetraene narrow significantly in a seeded free jet of ∼8 ppm octatetraene in helium (FWHM∼200 cm−1 for the room temperature static gas; FWHM∼35 cm−1 in the jet). Although absolute intensities of the vibronic bands are not determined, there is significant intensity in the origin, and the vibronic development involves only a few modes. Estimated translational, rotational, and vibrational temperatures of ∼1,<45, and <170 K, respectively, were achieved in the expansion. The major source of the observed linewidth is attributed to coupling of the 1 1Bu state to the lower 1Ag states.

Free-jet fluorescence excitation spectrum of t r a n s, t r a n s-1,3,5,7-octatetraene

The fluorescence excitation spectrum from 2980 to 2650 Å of trans, trans-1,3,5,7-octatetraene in a free jet has been measured monitoring emission in the region 3250 to 3500 Å. The vibronic bands of the 1 1Bu←1 1Ag (S2←S0) transition of octatetraene narrow significantly in a seeded free jet of ∼8 ppm octatetraene in helium (FWHM∼200 cm−1 for the room temperature static gas; FWHM∼35 cm−1 in the jet). Although absolute intensities of the vibronic bands are not determined, there is significant intensity in the origin, and the vibronic development involves only a few modes. Estimated translational, rotational, and vibrational temperatures of ∼1,&amp;lt;45, and &amp;lt;170 K, respectively, were achieved in the expansion. The major source of the observed linewidth is attributed to coupling of the 1 1Bu state to the lower 1Ag states.

ChemInform Abstract: SINGLE VIBRONIC LEVEL FLUORESCENCE FROM 1B3U PYRAZINE: THE ROLE OF FERMI RESONANCE AND DUSCHINSKI ROTATION

We report a study of the 1B3u←1Ag transition in pyrazine based on a combination of gas phase absorption and single vibronic level fluorescence spectra. Particular attention is paid to relative transition moments, especially where asymmetries exist between the intensities in the absorption and emission spectra. Band intensities and positions provide evidence for Fermi resonances and Duschinski rotations, but not for a symmetry change between the 1Ag and 1B3u states. Upper limits for displacements along several non‐totally symmetric normal coordinates are set, and a few new vibrational assignments are made.

Single vibronic level fluorescence from 1B3u pyrazine: The role of Fermi resonance and Duschinski rotation

We report a study of the 1B3u←1Ag transition in pyrazine based on a combination of gas phase absorption and single vibronic level fluorescence spectra. Particular attention is paid to relative transition moments, especially where asymmetries exist between the intensities in the absorption and emission spectra. Band intensities and positions provide evidence for Fermi resonances and Duschinski rotations, but not for a symmetry change between the 1Ag and 1B3u states. Upper limits for displacements along several non-totally symmetric normal coordinates are set, and a few new vibrational assignments are made.

Fluorescence excitation spectrum of the 1A u (nπ) ←1A g (0–0) band of oxalyl fluoride in a pulsed supersonic free jet

Oxalyl fluoride has been cooled to a rotational temperature of 0.17 K in a pulsed, supersonic jet. Individual rotational lines in the (0–0) band of the fluorescence excitation spectrum have been observed and assigned, and the rotational constants for both the 1Ag and 1Au states have been deduced. The pulsed nozzle used in these experiments can be operated with a far larger orifice diameter and at lower pressures than typically used in continuously operated nozzles, allowing greater cooling and higher jet densities while maintaining a low level of condensation.