Infrared spectrum of cyclic ozone: A theoretical investigation

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.

Valence Bond Alternative Yielding Compact and Accurate Wave Functions for Challenging Excited States. Application to Ozone and Sulfur Dioxide

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1¹B₂ and 2¹A₁ are the challenging ones. As the 1¹A₂, 1¹B₁, and 1¹B₂ states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2¹A₁ states and the 1¹A₁ ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1¹B₂ states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2¹A₁ ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2¹A₁ state of ozone and predicting some diradical character in the so-called "ionic" 1¹B₂ states.

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

The metastable ring structure of the ozone 1(1)A1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two (1)A1 states. In the present work, valence correlated energies of the 1(1)A1 state and the 2(1)A1 state were calculated at the 1(1)A1 open minimum, the 1(1)A1 ring minimum, the transition state between these two minima, the minimum of the 2(1)A1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 1(1)A1 state, the present calculations yield the estimates of (ring minimum-open minimum) ∼45-50 mh and (transition state-open minimum) ∼85-90 mh. For the (2(1)A1-(1)A1) excitation energy, the estimate of ∼130-170 mh is found at the open minimum and 270-310 mh at the ring minimum. At the transition state, the difference (2(1)A1-(1)A1) is found to be between 1 and 10 mh. The geometry of the transition state on the 1(1)A1 surface and that of the minimum on the 2(1)A1 surface nearly coincide. More accurate predictions of the energy differences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.

Electronic structure and bonding of ozone

The ground and low-lying states of ozone (O(3)) have been studied by multireference variational methods and large basis sets. We have constructed potential energy curves along the bending coordinate for (1,2) (1)A('), (1,2) (1)A("), (1,2) (3)A('), and (1,2) (3)A(") symmetries, optimizing at the same time the symmetric stretching coordinate. Thirteen minima have been located whose geometrical and energetic characteristics are in very good agreement with existing experimental data. Special emphasis has been given to the interpretation of the chemical bond through valence-bond-Lewis diagrams; their appropriate use captures admirably the bonding nature of the O(3) molecule. The biradical character of its ground state, adopted long ago by the scientific community, does not follow from a careful analysis of its wave function.

New theoretical investigations of the photodissociation of ozone in the Hartley, Huggins, Chappuis, and Wulf bands

We review recent theoretical studies of the photodissociation of ozone in the wavelength region from 200 nm to 1100 nm comprising four major absorption bands: Hartley and Huggins (near ultraviolet), Chappuis (visible), and Wulf (near infrared). The quantum mechanical dynamics calculations use global potential energy surfaces obtained from new high-level electronic structure calculations. Altogether nine electronic states are taken into account in the theoretical descriptions: four 1A', two 1A'', one 3A' and two 3A'' states. Of particular interest is the analysis of diffuse vibrational structures, which are prominent in all absorption bands, and their dynamical origin and assignment. Another focus is the effect of non-adiabatic coupling on lifetimes in the excited states and on the population of the specific electronic product channels.

The photoelectron spectrum of elusive cyclic-N3 and characterization of the potential energy surface and vibrational states of the ion

A potential energy surface is constructed for the ground X (1)A(1) electronic state of cyclic-N(3) (+) based on three-dimensional spline interpolation of ab initio points. The vibrational states of this molecular ion are calculated in the range up to 14 500 cm(-1) using hyperspherical coordinates and the coupled-channel (sector-adiabatic) approach. All the vibrational states are analyzed and assigned. The Franck-Condon overlaps of these states with the vibrational states of the neutral are calculated to predict the photoelectron spectrum of cyclic-N(3). Peak intensities are governed by the nodal structure of the vibrational wave functions and reflect the large geometric phase effect predicted for cyclic-N(3). Experimental validation may shed light on the existence of this elusive molecule and confirm the magnitude of the geometric phase effect.