Benchmarks of electronically excited states: basis set effects on CASPT2 results

Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.     

A CASSCF and CASPT2 study on the excited states of s-trans-formaldazine

The low-lying excited states of s-trans-formaldazine (H2CN-NCH2) have been investigated using the complete active space self-consistent field (CASSCF) and the multiconfigurational second-order perturbation (CASPT2) methods. The vertical excitation energies have been calculated at the state-average CASSCF and multistate CASPT2 levels employing the cc-pVTZ basis set. The photodissociation mechanisms starting from the S1 state have been determined. The lowest energy points along the seams of surface intersections have been located in both the Franck-Condon region and the N-N dissociation pathway in the S1 state. Once the system populates the S1 state, in the viewpoint of energy, the radiationless decay via S1/S0(3) conical intersection followed by the N-N bond fission in the ground-state is more favorable in comparison with the N-N dissociation process in the S1 state. A three-surface crossing region (S1/T1/T2), where the S1, T1, and T2 states intersect, was also found. However, the intersystem crossing process via S1/T1/T2 is not energetically competitive with the internal conversion via S1/S0(3).     

Excited states of acetylene: a CASPT2 study

Valence and low-lying Rydberg states of acetylene (C₂H₂) are reexamined in the singlet as well as in the triplet manifold. The major goal of this work is a better understanding of the valence states that contribute to the low-energy electron-energy-loss spectrum recorded under conditions where transitions to triplet states are enhanced. An appropriate theoretical treatment of these states has to include the low-lying Rydberg states because of their energetic proximity to some of the valence states. The CASSCF/CASPT2 method provides a suitable framework for such a task. For some important states the geometry was optimized at the CASPT2 level to allow a comparison with the results of other highly accurate methods that have been applied to acetylene in the past. Received: 11 June 1998 /Accepted: 30 July 1998 / Published online: 19 October 1998     

Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3

A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.     

A CASSCF/CASPT2 study on the low-lying excited states of HSiCN, HSiNC and their ions

Equilibrium geometries of low-lying electronic states of cyanosilylene (HSiCN), isocyanosilylene (HSiNC), and their ions have been investigated using the complete active space self-consistent field (CASSCF) approach. The harmonic vibrational frequencies on the optimized geometries were calculated using the multiconfiguration linear response (MCLR) method. Taking the further correlation effects into account, the complete active space perturbation theory of second-order (CASPT2) was carried out for the energetic correction. The CASPT2 calculations have been performed to obtain the vertical excitation energies of selected low-lying excited states of HSiCN and HSiNC. Computed results show that the singlet-triplet splittings are calculated to be 0.99 and 1.30 eV for HSiCN and HSiNC, respectively. The vertical excitation energies of the lowest singlet and triplet excited states in HSiCN are lower than those in HSiNC. The first vertical ionization energy of HSiCN (10.04 eV) is higher than that of HSiNC (9.97 eV). The ground-state adiabatic electron affinities are found to be rather high, and the value of HSiCN (1.85 eV) higher than that of HSiNC (1.52 eV). The existences of dipole-bound excited negative ion states have been discovered within HSiCN and HSiNC.     

CASPT2 study of the decomposition of nitrosomethane and its tautomerization reactions in the ground and low-lying excited states

The dissociation reaction of nitrosomethane into methyl and nitric oxide and the tautomerization reactions to formaldehyde oxime, nitrone, and methoxy nitrene have been studied with the second-order multiconfigurational perturbation theory (CASPT2) by the computation of numerical energy gradients. The prevailing reactions in both the ground and the excited states are dissociations. The structures of the ground and excited states are compared with the corresponding complete active space SCF (CAS-SCF) geometries. It is found that changes in the individual bond lengths are rather large (0.01-0.02 A), while the character and energetics of the CASPT2 optimizations remain similar to the CAS-SCF values.     

Low-lying electronic states of HNCS and its ions: a CASSCF/CASPT2 study

Complete active space self-consistent-field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) calculations in conjunction with the ANO-L basis set were performed to investigate systematically the low-lying electronic states of HNCS and its ions in C _s symmetry. Our highly accurate calculation indicated that theoretically determined geometric parameters and harmonic vibrational frequencies for the ground-state X ¹A′ are in good agreement with observed experimental data. The geometry of triplet HNCS is clearly favored C ₁ symmetry, and the relative energy is predicted to be 3.000 eV (69.2 kcal/mol). The vertical transition energies for the selected excited states of HNCS were calculated at CASSCF/CASPT2/ANO-L level of theory based on CASSCF optimized geometry. Except for a few linear states of X ²Π (1²A′, 1²A″), 1⁴Σ⁻ (1⁴A″), and 1²Σ⁺ (3²A′) states of HNCS⁺, our results confirmed that the majority of excited states are twisted trans-bend structures. The existence of bound excited anion states has been found for the first time in HNCS⁻. A more elaborate examination of ionization potential of HNCS (AIP, VIP) than previous reports has been presented.     

Ground and excited state CASPT2 geometry optimizations of small organic molecules

A method for computing second-order multiconfigurational perturbation theory (CASPT2) energy gradients numerically has been implemented and applied to a range of elementary organic chromophores, including 1,3 butadiene, acrolein, and two protonated Schiff bases. Geometries of ground and excited states-as well as conical intersections-are compared with the corresponding CASSCF structures, illustrating the effect of including the correction for dynamical electron correlation. It is shown that the differences between the two methods are not readily categorized, but that, while individual changes in bond lengths can be quite large ( approximately 0.01-0.02 A), the natures and CASPT2 energetics of the structures remain similar. Exceptions to this tend to be systems that have a strong ionic character and that are not well described at the CASSCF level. Basis set effects (double- vs. triple-zeta) were examined for a limited number of examples, and found to be quite dramatic at both levels of theory.     

Dibenzo-p-dioxin. An ab initio CASSCF/CASPT2 study of the pi-pi* and n-pi* valence excited states

The pi-pi* and n-pi* valence excited states of dibenzo-p-dioxin (DD) were studied via the complete active space SCF and multiconfigurational second-order perturbation theory employing the cc-pVDZ basis set and the full pi-electron active spaces of 16 electrons in 14 active orbitals. The geometry and harmonic vibrational wavenumbers of the ground state correlate well with the experimental and other theoretical data. In particular, significant improvements over previously reported theoretical results are observed for the excitation energies. All of the pi-pi* excited states exhibit planar D(2h)minima. Thus no evidence was found for a C(2v) butterfly-like relaxation, although the wavenumbers of the b(3u) butterfly flapping mode proved exceedingly low in both the ground S(0)((1)A(g)) and the lowest dipole allowed excited S(1)((1)B(2u)) state. The calculations of oscillator strengths established the 2(1)B(2u) <-- 1(1)A(g) and 2(1)B(1u) <-- 1(1)A(g) transitions as by far the most intense, whereas the only allowed of the n-pi* transitions ((1)B(3u)) should possess only a modest intensity. Studies into dependence of the oscillator strengths on the extent of the butterfly-like folding showed that the electronic spectrum is more consistent with a folded equilibrium geometry assumed by DD in solution.     

Multiconfigurational perturbation theory (CASPT2) applied to the study of the low-lying singlet and triplet excited states of cyclopropene

The electronic spectrum of cyclopropene has been studied using multiconfigurational second-order perturbation theory (CASPT2) with extended ANO-type basis sets. The calculation comprises two valence states and the 3s, 3p, 3d members of the Rydberg series converging to the π and σ ionization limits. A total of twenty singlet and twenty triplet excited states have been analyzed. The results confirm the valence nature of the lowest energy singlet-singlet band and yield a conclusive assignment: the first dipole-allowed transition in cyclcopropene is due to absorption to a (σ → π*) state. The (π → π*) (V) state is interleaved among a number of Rydberg states in the most intense band of the system. The remaining spectral bands are due to Rydberg transitions of higher energy. The two lowest singlet-triplet transitions involve the same valence states. The results are in agreement with available experimental data and provide a number of new assignments of the experimental spectra.     

A theoretical investigation of the excited states of OCLO radical, cation, and anion using the CASSCF/CASPT2 method

Using the complete active space self-consistent field method with a large atomic natural orbital basis set, 10, 13, and 9 electronic states of the OClO radical, OClO(+) cation, and OClO(-) anion were calculated, respectively. Taking the further correlation effects into account, the second-order perturbation (CASPT2) calculations were carried out for the energetic calibration. The photoelectron spectroscopy of the OClO radical and OClO(-) anion were extensively studied in the both case of the adiabatic and vertical ionization energies. The calculated results presented the relatively complete assignment of the photoelectron bands of the experiments for OClO and its anion. Furthermore, the Rydberg states of the OClO radical were investigated by using multiconfigurational CASPT2 (MS-CASPT2) theory under the basis set of large atomic natural orbital functions augmented with an adapted 1s1p1d Rydberg functions that have specially been built for this study. Sixteen Rydberg states were obtained and the results were consistent with the experimental results.     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

Geometries, electronic structures, and excited states of UN2, NUO+, and UO 2 2+ : a combined CCSD(T), RAS/CASPT2 and TDDFT study

The ground- and excited-state geometries and electronic structures of the isoelectronic series of molecules UN₂, NUO⁺, and UO ₂ ²⁺ are investigated by using relativistic density functional theory (DFT) and ab initio wavefunction theory (WFT). Scalar relativistic and spin?Corbit-coupled quantum chemical methods at the CASPT2, RASPT2, CCSD(T), DFT and TDDFT levels are applied. Relativistic effects as elucidated by Pekka Pyykk? play an important role in these uranium compounds, in particular for the excited states. The three molecular species exhibit significantly different spectroscopic properties, concerning their excitation energies, bond lengths and vibrations. Density functional approaches yield qualitatively correct results for the ground states and the valence????U.7s,6d excited states. However, the performance of TDDFT for valence????U.5f type excitations (in particular of UN₂ and NUO⁺) is less satisfactory, indicating the importance of the self-interaction correction for such excitations.     

The excited states of allene

Excited states of allene are calculated using virtual orbitals from a Gaussian SCF calculation on the ground state. The ground state ionization potential is predicted to be 10.14 eV. Although the calculated transition energies are too high, the spectrum is predicted to consist of 3 weak transitions followed by a strong transition at shorter wavelength, in good qualitative agreement with experiment. States of the flattened (D _2h) molecule were also studied. The rotation barrier of the ground state is predicted to be 3.12 eV. The lowest triplet state is predicted to be planar.

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Zusammenfassung Aus einer SCF Rechnung mit Gauß-Funktionen für den Grundzustand des Allens werden die virtuellen Orbitale für die Berechnung angeregter Zustände übernommen. Das Ionisationspotential des Grundzustands ergibt sich dabei zu 10,14 eV. Die Rechnungen zeigen, daß das Spektrum aus drei schwachen Übergängen und einem starken Übergang kürzerer Wellenlänge besteht. Dies steht in guter Übereinstimmung mit dem experimentellen Befund, obwohl die Übergangsenergien zu hoch berechnet werden. Die Zustände des Moleküls mit der Symmetrie D _2h werden studiert. Die Energieschranke für die Rotation wird zu 3,12 eV berechnet und der tiefste Triplett-Zustand als eben vorausgesagt.

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Résumé Calcul des états excités de l'aliène à l'aide des orbitales virtuelles fournies par un calcul SCF en gaussiennes sur l'état fondamental. Le calcul prédit un potentiel d'ionisation de 10.14 eV. Les énergies de transition caculées sont trop hautes mais le spectre calculé consiste en 3 transitions peu intenses suivies par une transition intense à plus courte longuer d'onde, ce qui est en bon accord qualitatif avec l'expérience. On a aussi étudié les états de la molécule «aplatie» (D _2h). La barrière de rotation est de 3.12 eV dans l'état fondamental. L'état triplet le plus bas devrait être plan.

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Work supported by the U.S. Army Research Office —Durham.     

The valence and Rydberg excited states of CH2: A theoretical exploration

Using the completed active space second‐order perturbation (CASPT2) method, valence and Rydberg excited states of CH₂ molecule are probed with the large atomic natural orbital (ANO‐L) basis set. Five states are optimized and the geometric parameters are in good agreement with the available data in literatures, furthermore, the state of 2¹B₁ is obtained for the first time. Valence and Rydberg excited states of CH₂ are also calculated for the vertical transitions with the ANO‐L+ basis set that is constructed by adding a set of 1s1p1d Rydberg orbitals into the ANO‐L basis set. Two Rydberg states of the p?³A₂ and r?³B₁ at 9.88 and 10.50 eV are obtained for the first time, and the 3a₁ → 3d_yz nature of the state p?³A₂ and the 3a₁ → d_x2?y2 nature of the state r?³B₁ are confirmed. © 2012 Wiley Periodicals, Inc.     

CASPT2 study on low‐lying states of HMgO and HOMg

The HMgO and magnesium monohydroxide (HOMg) have been reinvestigated using the complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO levels. The ground and the first excited states of HMgO are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOMg is X²Σ⁺ state. The A²Π state of HOMg has unique imaginary frequency. A bent local minimum M1 was found for the first time along the 1²A″ PES and the A²Π state of HOMg should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HMgO bond angle. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Theoretical computation of low‐lying electronic states of HCNS: A CASPT2 study

Complete active space self‐consistent field (CASSCF) and complete active space second‐order perturbation theory (CASPT2) calculations in conjunction with the aug‐cc‐pVTZ basis set have been used to investigate the low‐lying electronic states of thiofulminic acid (HCNS), HCNS⁺, and HCNS^?. The result of geometry optimization using CASPT2/aug‐cc‐pVTZ shows that theoretically determined geometric parameters and harmonic vibrational frequencies for the HCNS ground state X¹Σ⁺(X¹A′) are in agreement with previous studies. The ionization energies, the electron affinity energies, the adiabatic excitation energies, and vertical excitation energies have been calculated and the corresponding cation and anion states are identified. By calculating adiabatic electron affinity, the states of HCNS^? have been identified to contain both π orbital states (X²A′ and 1²A″) and dipole‐bond states (1⁴A′ and 1⁴A″). © 2012 Wiley Periodicals, Inc.     

CASPT2 study on low‐lying states of HBN and HNB radicals

In this study, some low‐lying states of the HBN and HNB radicals have been studied using multiconfiguration second‐order perturbation theory. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASPT2/cc‐pVQZ level. The ground and the first excited states of HBN were predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HNB is X²Σ⁺ state. The A²Π state of HNB has unique imaginary frequency, which was different from the previously published results. A bending local minimum M1 was found for the first time along the 1²A″ PES, and the A²Π state of HNB should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions for HBN ? HNB were calculated as a function of HBN bond angle. By comparing the CASPT2 and CASSCF calculated results, we concluded that the influence of the dynamic electron correlation on HBN ? HNB system is not large. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical studies on excited states of Ne2

Previously reported potential curves for 0 _g ^? (³ P ₀) and 0 _u ^? (³ P ₀) of Ne₂ obtained from large-scale configuration-interaction calculations supplemented by semiempirical spin-orbit calculations are compared with potential curves deduced from experimental studies by Beyer and Haberland. Although the agreement between curves is very good, the assignment of states is opposite.Ab initio spin-orbit coupling matrix elements were calculated based on large CI wavefunctions for states dissociating to Ne + Ne^*(3s). It was found that they hardly change between 5 and 20a₀.Ab initio spin-orbit corrected potential curves differ little from previous curves relying on the semiempirical treatment of spin-orbit coupling, and all former conclusions remain essentially unchanged.