Benchmarking NMR indirect nuclear spin-spin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD

Accurate calculations of NMR indirect nuclear spin-spin coupling constants require especially optimized basis sets and correlated wave function methods such as CCSD or SOPPA(CCSD). Both methods scale as N(6), where N is the number of orbitals, which prevents routine applications to molecules with more than 10-15 nonhydrogen atoms. We have therefore developed a modification of the SOPPA(CCSD) method in which the CCSD singles and doubles amplitudes are replaced by CC2 singles and doubles amplitudes. This new method, called SOPPA(CC2), scales only as N(5), like the original SOPPA-method. The performance of the SOPPA(CC2) method for the calculation of indirect nuclear spin-spin coupling constants is compared to SOPPA and SOPPA(CCSD) employing a set of benchmark molecules. We also investigate the basis set dependence by employing three different basis sets optimized for spin-spin coupling constants, namely the HuzIV-su4, ccJ-pVTZ, and ccJ-pVQZ basis sets. The results of the corresponding CCSD calculations are used as a theoretical reference.     

TD-CI simulation of the electronic optical response of molecules in intense fields: comparison of RPA, CIS, CIS(D), and EOM-CCSD

A number of different levels of theory have been tested in TD-CI simulations of the response of butadiene interacting with very short, intense laser pulses. Excitation energies and transition dipoles were calculated with linear-response time-dependent Hartree-Fock (also known as the random phase approximation, RPA), configuration interaction in the space of single excitations (CIS), perturbative corrections to CIS involving double excitations [CIS(D)], and the equation-of-motion coupled-cluster (EOM-CC) method using the 6-31G(d,p) basis set augmented with n = 0-3 sets of diffuse sp functions on all carbons and only on the end carbons [6-31 n+ G(d,p) and 6-31(n+)G(d,p), respectively]. Diffuse functions are particularly important for transitions between the pseudocontinuum states above the ionization threshold. Simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. Depending on the basis set, up to 500 excited states were needed for the simulations. Under the conditions selected, the response was too weak with the 6-31G(d,p) basis set, and the difference between levels of theory was more pronounced. When two or three set of diffuse functions were included on all of the carbons, the RPA, CIS, and EOM-CC results were comparable, but the CIS(D) response was too large compared to the more accurate EOM-CC calculations. Even though the frequency of the pulse is not resonant with any of the ground-to-excited transitions, excitations to valence and pseudocontinuum states occur readily above a threshold in the intensity.     

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.     

Calculations of the low-lying excited states of the TiO(2) molecule

We present calculations of the lowest excited electronic states of the TiO(2) molecule. These are computed using several correlated wavefunction response based methods, as well as time-dependent density functional response theory using a range of functionals. Surprisingly lower cost wavefunction based methods, in particular the second-order CC2 and CIS(D) methods, completely fail to describe the lowest (1)B(2) and (1)A(2) states of the molecule. Density functional methods fare better but still show considerable variation amongst functionals. Thus TiO(2) provides a strenuous test for correlated excited state methods.     

Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations

Stacking energies in low-energy geometries of pyrimidine, uracil, cytosine, and guanine homodimers were determined by the MP2 and CCSD(T) calculations utilizing a wide range of split-valence, correlation-consistent, and bond-functions basis sets. Complete basis set MP2 (CBS MP2) stacking energies extrapolated using aug-cc-pVXZ (X = D, T, and for pyrimidine dimer Q) basis sets equal to -5.3, -12.3, and -11.2 kcal/mol for the first three dimers, respectively. Higher-order correlation corrections estimated as the difference between MP2 and CCSD(T) stacking energies amount to 2.0, 0.7, and 0.9 kcal/mol and lead to final estimates of the genuine stacking energies for the three dimers of -3.4, -11.6, and -10.4 kcal/mol. The CBS MP2 stacking-energy estimate for guanine dimer (-14.8 kcal/mol) was based on the 6-31G(0.25) and aug-cc-pVDZ calculations. This simplified extrapolation can be routinely used with a meaningful accuracy around 1 kcal/mol for large aromatic stacking clusters. The final estimate of the guanine stacking energy after the CCSD(T) correction amounts to -12.9 kcal/mol. The MP2/6-31G(0.25) method previously used as the standard level to calculate aromatic stacking in hundreds of geometries of nucleobase dimers systematically underestimates the base stacking by ca. 1.0-2.5 kcal/mol per stacked dimer, covering 75-90% of the intermolecular correlation stabilization. We suggest that this correction is to be considered in calibration of force fields and other cheaper computational methods. The quality of the MP2/6-31G(0.25) predictions is nevertheless considerably better than suggested on the basis of monomer polarizability calculations. Fast and very accurate estimates of the MP2 aromatic stacking energies can be achieved using the RI-MP2 method. The CBS MP2 calculations and the CCSD(T) correction, when taken together, bring only marginal changes to the relative stability of H-bonded and stacked base pairs, with a slight shift of ca. 1 kcal/mol in favor of H-bonding. We suggest that the present values are very close to ultimate predictions of the strength of aromatic base stacking of DNA and RNA bases.     

DFT and CIS(D) theoretical study on the ground and excited states of pentanitrogen cation

Different isomers of N₅⁺ were modeled at DFT(PBE0)/aug-cc-pV(Q + d)Z, and their ground(transition) state characteristics were assessed through frequency calculations. Single-point energies were accomplished at PBE0/aug-cc-pV(5 + d)Z. Nonlinear optical susceptibilities (NLO) of isomers were accomplished using Firefly, while the linear optical invariant was examined using the finite-field method, Firefly, and modified dipole field tensor in the presence of two different screening factors. The excited states, singlets and triplets, of were modeled at the CIS and CIS(D) and then their optical parameters were estimated at TDFT(PBE0)/aug-cc-pV(Q + d)Z using Firefly. The singlet is found the most stable isomer, with the inversional rate constant larger than that of the Cs isomer and high energy barrier with the triplet counterpart. Isomers 2 , 3 , and 4 are found local minima, while 5 and 6 are saddle points: transition states between equivalent invertomers. Energy calculations of the singlet and triplet isomers were in excellent agreement with the literature. An excellent correlation is found between the average polarizability and the impulse factor. Substantial variations were found between the singlet and triplet excited states in terms of energy, geometry, and optical properties from one side and with from the other side. Reactivity indices showed that N1 and N5 are the optimum nucleophilic and electrophilic reactivity sites.     

The structure of BO2 in its ground and low-lying excited states from ab initio SCF RHF AND CI calculations

Potential curves for the X²Π_g, A²Π_u, B²Σ⁺_u and C²Σ_g⁺ electronic states of BO₂ were calculated at ab initio SCF RHF and configuration interaction (CI) level. The results obtained are consistent with a linear molecular model for all states considered. The calculated structural parameters and transition energies are in good agreement with relevant experimental data.     

Density functional theory and multireference configuration interaction studies on low-lying excited states of TiO2

Using density functional theory at the BPW916-311+G(3df) level, optimized geometries and energies of the lowest singlet, triplet, and quintet A(1), A(2), B(1), B(2)(C(2v)) states of the TiO(2) molecule were obtained. TiO(2) has a (1)A(1) ground state in C(2v) symmetry. Adiabatic excitation energies of the low-lying singlet and triplet states range from 2.1 to 3.0 eV. The (1,3)A(2) states optimize at bond angles of about 140 degrees , lying only 0.06 eV below linear (1,3)Delta(u), whereas (1,3)B(1) and (1,3)B(2), with bond angles of 120 degrees and 96 degrees , respectively, lie 0.3-0.4 eV below the respective (1,3)Pi(u) or (1,3)Delta(u) states. Minima with short O-O distances of approximately 1.46 A, at energies of 4.2 and 4.7 eV, were found for (1)A(1) and (3)A(1). The C(2v) minima of the lowest (1)B(1) and (3)B(1) states are saddle points, suggesting lower-energy structures in C(s) symmetry. The C(2v) quintet states start at energies of 5.7 eV. Multireference configuration interaction (MRCI) methods, employing a polarized valence triple-zeta basis set, lead to similar geometries and energies. MRCI vertical excitation energies up to 4.6 eV and oscillator strengths are given. The calculated excitation energy of 2.2 eV for (1)B(2) agrees well with 2.3 eV from a fluorescence spectrum. The vertical electron detachment energy of TiO(2) (-) is 1.5 eV, in good agreement with 1.6 eV from anion photoelectron spectroscopy. An observed second photoelectron band corresponds to (1)B(2) and/or (3)B(2), but the assignment of a third band could not be verified. Vibrational frequencies, ionization energies, electron affinities, and dissociation energies are given.     

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.     

Time-dependent density functional theory benchmarking for the calculations of atomic spectra: efficiency of exc-ETDZ basis set

We present a time-dependent density functional theory (TD-DFT) benchmarking of recently constructed basis set, namely exc-ETDZ (Guevara et al. in J Chem Phys 131: 064104, 2009) for predicting the atomic spectra of the first-row atoms. A systematic testing with 31 density functional methods has been performed to see whether convincing performance of this basis set carries over the TD-DFT formalism. The efficiency of exc-ETDZ basis set for reproducing atomic spectra has been compared with Pople- and Dunning-style basis sets. We focused on the atomic low-lying valence excited states with single excitation character for our benchmarking, and the calculated excitation energies were compared to experimental data. On average, the functionals providing the best match with exc-ETDZ basis are BMK, BH&HLYP and ωB97. Moreover, on the basis of comparison between the results of these superior functionals with CIS(D) estimates, it turned out that TD-DFT and CIS(D) errors are of the same order of magnitude, once the exc-ETDZ basis set is used. Finally, the results of present study indicate that different functionals show results that are highly dependent on the atomic configuration as well as the basis set.     

Accuracy and efficiency of atomic basis set methods versus plane wave calculations with ultrasoft pseudopotentials for DNA base molecules

Recent results from Preuss et al. (J Comput Chem 2004, 25, 112) on DNA base molecules, obtained by plane wave density functional calculations using ultrasoft pseudopotentials, are compared with calculations using Gaussian basis sets. Bond lengths and angles agree closely, but dihedral angles and vibrational frequencies show significant differences. The Gaussian basis calculations are at least an order of magnitude more efficient than the plane wave/ultrasoft pseudopotential calculations at a similar level of accuracy; the advantage is even larger if the Fourier Transform Coulomb method is used. To obtain definite benchmark values, the geometries of the four DNA bases were optimized at the MP2 level with large basis sets, up to cc-pVQZ and aug-cc-pVTZ.     

Ab initio calculations on low-lying electronic states of SnCl(2)- and Franck-Condon simulation of its photodetachment spectrum

Geometry optimization and harmonic vibrational frequency calculations have been carried out on low-lying doublet and quartet electronic states of stannous (tin(II)) dichloride anion (SnCl(2)(-)) employing the CASSCF and RCCSD(T) methods. The small-core fully-relativistic effective core potential, ECP28MDF, was used for Sn in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. The ground electronic state of SnCl(2)(-) is determined to be the X(2)B(1) state, with the A(2)B(2) and ?(4)Sigma state, calculated to be ca. 1.50 and 2.72 eV higher in energy respectively. The electron affinities of the X(1)A(1) and ?(3)B(1) states of SnCl(2) have been computed to be 1.568+/-0.007 and 4.458+/-0.002 eV respectively, including contributions of core correlation and extrapolation to the complete basis set limit. The SnCl(2) (X(1)A(1)) + e <-- SnCl(2)(-) (X(2)B(1)) and SnCl(2) (?(3)B(1)) + e <-- SnCl(2)(-) (X(2)B(1)) photodetachment bands have been simulated with computed Franck-Condon factors, which include an allowance for anharmonicity and Duschinsky rotation.     

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.     

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.     

A mixed basis set of slater and gaussian functions for molecular calculations

A procedure for using simultaneously Slater and Gaussian basis functions in molecular calculations is presented here. The analytic expressions of the integral prototypes involving both Slater and Gaussian functions are explicitly derived.     

SCF calculations for H 2 + , Li 2 + and LiH+ with atomic basis sets enlarged by bond functions

To simulate the charge distortion in the formation of a molecule from the separated atoms, a set of concentrics-type Gaussian functions is placed on the internuclear axis in addition to thes-type atomic basis functions to construct the molecular orbital for the one valence-electron systems H ₂ ⁺ , Li ₂ ⁺ and LiH⁺. This simple model gives 90.1%, 75.2% and 61.7%, respectively, of the improvement over minimal basis relative to Hartree-Fock energies.Supported in part by a research grant to Rice University from the Robert A. Welch Foundation.     

Quantum-chemical calculations for paramagnetic 13C NMR chemical shifts of iron-bound cyanide ions of iron porphyrins in ground and low-lying excited states containing ferric (dxy)2(dxz,yz)3 and (dxy)1(dxz,yz)4 configurations

Accurate quantum-chemical calculations were carried out for bis(cyanide) and cyanide-imidazole Fe(III) porphyrins in the ground and low-lying excited states including both the ferric (dxy)2(dxz,yz)3 and (dxy)1(dxz,yz)4 configurations. The trans-ligand effect on the paramagnetic 13C NMR chemical shifts of the iron-bound 13CN- was well reproduced by the present calculations. Further, in bis(cyanide)(meso-tetraethyl) Fe(III) porphyrin, which has a ruffled porphyrin ring, the (dxy)1(dxz,yz)4 configuration is included in the ground state, and the alternative (dxy)2(dxz,yz)3 configuration is located closely in energy to the ground state. Ruffling of porphyrin rings extremely affects the 13C chemical shift of iron-bound CN in the (dxy)1(dxz,yz)4 configuration but not in the (dxy)2(dxz,yz)3 configuration.     

Ground and low-lying excited states of propadienylidene (H2C=C=C:) obtained by negative ion photoelectron spectroscopy

A joint experimental-theoretical study has been carried out on electronic states of propadienylidene (H(2)CCC), using results from negative-ion photoelectron spectroscopy. In addition to the previously characterized X(1)A(1) electronic state, spectroscopic features are observed that belong to five additional states: the low-lying ?(3)B(1) and b(3)A(2) states, as well as two excited singlets, ?(1)A(2) and B(1)B(1), and a higher-lying triplet, c(3)A(1). Term energies (T(0), in cm(-1)) for the excited states obtained from the data are: 10,354±11 (?(3)B(1)); 11,950±30 (b(3)A(2)); 20,943±11 (c(3)A(1)); and 13,677±11 (?(1)A(2)). Strong vibronic coupling affects the ?(1)A(2) and B(1)B(1) states as well as ?(3)B(1) and b(3)A(2) and has profound effects on the spectrum. As a result, only a weak, broadened band is observed in the energy region where the origin of the B(1)B(1) state is expected. The assignments here are supported by high-level coupled-cluster calculations and spectral simulations based on a vibronic coupling Hamiltonian. A result of astrophysical interest is that the present study supports the idea that a broad absorption band found at 5450 ? by cavity ringdown spectroscopy (and coincident with a diffuse interstellar band) is carried by the B(1)B(1) state of H(2)CCC.     

Othrogonality and optimization of the basis for the energies of excited states of molecules

We developed a method of taking into account orthogonality, which reduces the conditional minimization problem in the variational calculation of the energy of an excited state to a problem without conditions. The method makes it possible to adjust the basis under an electronic state by minimizing the energy of the excited state with respect to a set of nonlinear parameters. The approach is based on the construction of a modified Hamiltonian, for which an approximate ground-state vector becomes an eigenvector. We discuss the features of the method associated with the approximate nature of the ground-state wave function. The energies of excited states of the molecules He ₂ ²⁺ and H₂ are calculated and analyzed. The excited-state energies obtained using small Gaussian basis agree closely with the results obtained with large basis consisting of James-Coolidge functions.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 4, pp. 467–471, July–August, 1989.