Complete Active Space Multiconfiguration Self-consistent Field Research Articles

A time-dependent density-functional theory and complete active space self-consistent field method study of vibronic absorption and emission spectra of coumarin.

Time-dependent density-functional theory (TD-DFT) and complete active space multiconfiguration self-consistent field (CASSCF) calculations have been used to determine equilibrium structures and vibrational frequencies of the ground state and several singlet low-lying excited states of coumarin. Vertical and adiabatic transition energies of S1, S2, and S3 have been estimated by TD-B3LYP and CASSCF/PT2. Calculations predict that the dipole-allowed S1 and S3 states have a character of (1)(ππ*), while the dipole-forbidden (1)(nπ*) state is responsible for S2. The vibronic absorption and emission spectra of coumarin have been simulated by TD-B3LYP and CASSCF calculations within the Franck-Condon approximation, respectively. The simulated vibronic spectra show good agreement with the experimental observations available, which allow us to reasonably interpret vibronic features in the S0→S1 and S0→S3 absorption and the S0←S1 emission spectra. Based on the calculated results, activity, intensity, and density of the vibronic transitions and their contribution to the experimental spectrum profile have been discussed.

ChemInform Abstract: Geometries and Energies of GeHn and GeH+ n (n = 1-4)

Complete active space MCSCF (multiconfiguration self‐consistent field) (CASSCF) followed by second‐order configuration interaction (SOCI) and multireference singles and doubles CI (MRSDCI) are carried out on the ground states of GeHn and GeH+n (n=1–4). The equilibrium geometries of these species, adiabatic ionization potentials, and stepwise bond energies [De(Hn−1Ge–H) and De(Hn−1Ge+–H)] are calculated. The ground sate of GeH+4 is a Jahn–Teller distorted 2A1(C2v) state with a GeH+2⋅H2 complex structure. The adiabatic ionization potentials (IPS) of GeHn exhibit even–odd alternation. GeH4 is the most stable among the neutral GeHn species while GeH+3 is the most stable of the GeH+n.

Electronic states and potential energy curves of InN 2, In 2N, and their ions

Potential energy curves of low-lying electronic states of InN 2, In 2N, and their cations and anions are investigated by the complete active space multi-configuration self-consistent field (CASSCF) followed by multi-reference singles + doubles configuration interaction (MRSDCI) computations. The neutral InN 2 and In 2N exhibit linear 2Π and 2 Σ u + ground states, respectively. The InNN + cation exhibits a linear C ∞v ground state whereas In 2N + ion exhibits two nearly-degenerate singlet and triplet ground states. Whereas In 2N − is strongly bound with an adiabatic electron affinity of 2.07 eV, the electron affinity of InNN is only 0.2 eV.

Electronic states for Al 2As 2 and its ions

Low-lying electronic states of Al 2As 2 and its ions are investigated using the complete active space multiconfiguration self-consistent field(CASSCF) method and the density functional theory (DFT:B3LYP). The vibrational frequencies and IR intensities of the electronic states are calculated and presented at the DFT level, which conforms that these states have stable minima at their geometry structures. Results suggest the rhombus structure is the equilibrium geometry for the ground states and most excited states of Al 2As 2 and its ions. The adiabatic ionization potential and other properties of Al 2As 2 are predicted and discussed.

Spectroscopic properties for Al 2As, AlAs 2, and their ions

Density functional theory (DFT:B3LYP) and complete active space multiconfiguration self-consistent field (CASSCF) calculations are performed on the low-lying electronic states of AlAs 2, Al 2As, and their ions. The optimized geometries of the electronic states of these clusters at the DFT level are found to be close to the results at the CASSCF level. On the basis of our computed results, the adiabatic ionization potentials, and the ground states of AlAs 2, Al 2As, and their ions are evaluated and discussed.

Valence ab initio calculation of the potential energy curves for Ca–rare gas van der Waals molecules

Adiabatic potential curves for the ground state and several low-lying excited states of the calcium atom interacting with rare gas (RG) atoms have been obtained in the ΛS coupling scheme from valence ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/complete-active-space multireference second-order perturbation theory (CASPT2) calculations. In the calculations the Ca2+ and RG8+ atomic cores are represented by scalar-relativistic energy-consistent pseudopotentials. Core polarization and core-valence correlation have been accounted for by adding a core polarization potential (CPP) to the Hamiltonian. Moreover, the closed-shell single-reference coupled-cluster approach with single and double excitations including a perturbative treatment of triple excitations (CCSD(T)) has been used to obtain more accurate ground-state potential curves for the species. The transition dipole moments from the ground state to the excited 1Σ and 1Π states correlating with the (3d)1D and (4p)1P Ca terms have been evaluated as a function of R. Fine structure of the molecular terms has also been studied using a semi-empirical two-electron spin–orbit pseudopotential for the Ca atom.

A theoretical study of potential energy curves and spectroscopic constants of VC

Potential energy curves for the various low-lying electronic states of VC have been studied using complete active space multi-configuration self-consistent field (CASMCSCF) followed by first-order and multireference singles and doubles configuration interaction (FOCI, MRSDCI) calculations. The MRSDCI calculations included up to 6 million configurations. Two very low-lying electronic states are found as candidates for the ground state of VC, namely a high spin state 4Δ and a low-spin 2Δ state, which is favoured at higher levels. A number of low-lying excited electronic states of VC are predicted, which are yet to be observed. The low-lying electronic states of VC are found to be ionic as inferred from the dipole moments and the charge density calculations. Electron donation and the back-donation process are suggested to be operative in the V-C bond formation.

Spectroscopic properties of Mo 2− and Mo 2+

Potential energy curves and spectroscopic constants for 30 electronic states of Mo 2 + together with the ground states of Mo 2 − anion and Mo 2 have been computed using the complete active space multiconfiguration self-consistent field (CASMCSCF) followed by the multireference singles + doubles configuration interaction (MRSDCI) calculations that included up to 44.4 million configurations. We have reported computed equilibrium distances ( r e), vibrational frequencies ( ω e) and energy separations ( T e). We have predicted several spectroscopic systems for Mo 2 +, which are yet to be observed and the electron affinity of Mo 2.

Spectroscopic properties of lead hexamer and its ions (Pb6, Pb6+, Pb6−)

We have computed the optimized geometries and energy separations of low-lying electronic states of the lead hexamer (Pb6) and its positive and negative ions. Our techniques have included high level relativistic electron correlation techniques such as complete active space multiconfiguration self-consistent field (CAS-MCSCF) method followed by large scale multireference singles plus doubles configuration interaction (MRSDCI) and relativistic configuration interaction (RCI) computations that included up to 16 million configurations. Our computed results have facilitated the assignment of the anion photodetachment spectra of Pb6− and also in the prediction of the properties of yet to be observed electronic states. A 1A1g tetragonal bipyramid structure (D4h symmetry) is found as the ground state for Pb6. The excitation energy, atomization energies, ionization potentials, and vertical and adiabatic electron affinities are computed and compared with the experimental results. We have assigned the observed X, A, B, C, D, and E states of the anion photoelectron spectra of Pb6−, and discuss spin–orbit versus Jahn-Teller effects.

Geometries and spectroscopic properties of silicon clusters (Si5, Si5+, Si5−, Si6, Si6+, and Si6−)

Ground and excited electronic states of the neutral, cationic, and anionic silicon pentamer and hexamer (Si5 and Si6) are investigated. Different geometries such as trigonal bipyramid (TBP; D3h), distorted-TBP (C2v), and edge-capped tetrahedron (ECT; C2v) for Si5 and tetragonal bipyramid (TEBP; D4h, D2h), edge-capped trigonal bipyramid (ECTBP; C2v) for Si6 were studied. We have employed a number of techniques such as large scale complete active-space multiconfiguration self-consistent field (CAS-MCSCF), mutireference singles+doubles configuration interaction (MRSDCI) computations up to 12 million configurations, Møller–Plesset (MP2) and coupled cluster singles and doubles+triple excitation estimate [CCSD(T)] techniques to investigate the low-lying electronic states, their geometries and energy separations of neutral, cationic and anionic Si5 and Si6. A A1g1 TEBP structure (D4h symmetry) is computed as the ground state for Si6, in accord with the previously suggested experimental assignments, while the Si5 cluster is found to have a TBP (D3h) ground state. The excitation energy, atomization energies, ionization potentials, and vertical and adiabatic electron affinities are computed and compared with the experimental results. Our computations of the excited states of these species have facilitated assignment of the anion X, A, and B bands of the photoelectron spectra of Si5− and Si6− observed by Neumark and co-workers.

Potential energy surfaces of Lawrencium and Nobelium dihydrides (LrH2 and NoH2)

It is demonstrated that the compounds of late actinides, namely Lawrencium and Nobelium surprisingly exhibit unusual nonactinide properties in that unlike other actinides the chemistry of these species is principally determined by the 7s and 7p orbitals rather than the 5f or 6d shells. Relativistic computations including electron correlation and spin–orbit effects using the complete-active space multiconfiguration self-consistent field followed by second-order and multireference relativistic configuration interaction (RCI) techniques are considered for the Lawrencium and Nobelium dihydrides as well the atoms. The ground and first excited states of Lawrencium and Nobelium arise from the 7s and 7p shells, and thus the potential energy surfaces of these species are unusual in having considerable 7p characteristics. Both molecules form stable bent ground states reminiscent of sp2 hybridization with equilibrium bond angles near 120°. The Lawrencium compounds exhibit unusual characteristics due to avoided crossings of the potential energy surfaces. As a result of spin–orbit coupling, the B22 state of LrH2 undergoes avoided crossing with the A12 state in the spin double group, which reduces the barrier for insertion of Lr into H2. The Nobelium compounds are shown to be considerably less stable compared to Lawrencium compounds due to the relativistic stabilization of the 7s shell of the Nobelium atom. It is shown that the barrier for insertion of Lr into H2 is lowered by relativity (spin–orbit coupling), while No has to surpass a larger barrier due to the relativistic stabilization of the 7s2 shell, which is not very reactive. Lawrencium is the only element in the actinide series with unusually low ionization potential, and NoH2 has an unusually large dipole moment of 5.9 Debye. It is suggested that the Lawrencium and Nobelium compounds should have periodic similarities to the thallium and radium compounds, respectively.

Ab initio calculations for the potential curves and spin-orbit coupling of Mg 2

The ground state and several low-lying excited states of the Mg2 dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A1Σu+ excited state of Mg2 is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants De, Re and ωe deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg2 have been evaluated as a function of internuclear separation.

Theoretical study of the electronic states of small cationic niobium clusters, Nbn+ (n=3–5)

Geometries and energy separations of the various low-lying electronic states of Nbn+ (n=3–5) clusters with different structural arrangements have been investigated. The complete active space multiconfiguration self-consistent field (CASMCSCF) method followed by the multireference singles plus doubles configuration interaction (MRSDCI) that included up to 13 million configuration spin functions have been used to compute several electronic states of these clusters. A A25 isosceles triangle geometry in C2v symmetry and a A′2 pyramid structure in Cs symmetry are computed as the ground states of Nb3+ and Nb4+ clusters, respectively. In the case of Nb5+, a A′1 state of distorted edge-capped tetrahedral structure (in Cs symmetry) was found to be the ground state. We also compared our MRSDCI results with density functional calculations. The dissociation and atomization energies have been calculated at the MRSDCI level and the results have been found to be in agreement with experimental findings.

Interaction of benzene (Bz) with Pt and Pt2: A theoretical study on Bz–Pt2, Bz2–Pt, Bz2–Pt2, and Bz3–Pt2 clusters

Extensive ab initio calculations have been carried out on benzene (Bz)–platinum complexes (Bz–Pt2, Bz2–Pt, Bz2–Pt2, and Bz3–Pt2) using a variety of computational techniques. Both physisorbed structures and energetically lower chemisorbed species were found. Complete active space multiconfiguration self-consistent field (CASMCSCF), multireference singles and doubles configuration-interaction (MRSDCI), density functional (DFT), and Møller–Plessett second order perturbation (MP2) calculations were employed to predict Bzm–Ptn structures. While the DFT and MP2 calculations also consistent with the MRSDCI techniques predict chemisorbed structures to be lower, the CASMCSCF method seems to favor physisorbed structures. The effect of spin-orbit coupling on the binding energies of complexes with the Pt atom and the Pt2 dimer were considered. The computed dissociation energies are consistent with the relative abundance of these clusters found in the time-of-flight mass spectra. The low-energy staircase structures of Bz2–Pt, Bz2–Pt2, and Bz3–Pt2 complexes found in this study could be electrically conducting.

Quasirelativistic valence ab initio calculation of the potential curves for the Zn–rare gas van der Waals molecules

Results of large scale valence ab initio calculations of the potential curves for the ground and several low lying excited states of the Zn–rare gas (RG) van der Waals molecules are reported. In the calculations, the Zn 20+ and RG 8+ cores are replaced by energy-consistent pseudopotentials which also account for scalar-relativistic effects and spin–orbit (SO) interaction. Potential energies in the ΛS coupling scheme have been obtained by means of valence ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/complete-active-space multireference second-order perturbation theory (CASPT2) calculations. On the other hand, the corresponding SO matrix has been calculated in a reduced CI space restricted to the CASSCF level. The final Ω potential curves are obtained by diagonalization of the modified SO matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, and particularly the derived spectroscopic parameters D e , R e and ω e for the ground and excited states of the Zn–RG complexes are discussed in the context of available experimental data. Quite reasonable agreement between the theoretical results and experimental data has been obtained for all Zn–RG pairs.

Theoretical study of the A30+ ← X10+ and B31 ← X10+ transitions in the Cd-rare gas van der Waals molecules

Excitation spectra arising from A 3 0 - ← X 1 0 + and B 3 1 ← X 1 0 + electronic transitions in the Cd-rare gas (RG) van der Waals molecules are calculated using newly obtained theoretical potential curves for these species. In the molecular structure calculations, Cd 20+ and RG 8+ cores are simulated by energy-consistent pseudopotentials which also account for scalar-relativistic effects and spin-orbit (SO) interaction within the valence shell. Potential energies in the AS coupling scheme have been obtained by means of ab initio complete-active-space multiconfiguration self consistent-field (CASSCF)/complete-active-space multireference second-order perturbation theory (CASPT2) calculations with a total 28 correlated electrons, while the SO matrix has been computed in a reduced Cl space restricted to the CASSCF level. The final Ω potential curves are obtained by diagonalization of the modified SO matrix (its diagonal elements before diagonalization substituted for the corresponding CASPT2 eigen-energies). The spectroscopic parameters for the ground and several excited states of the Cd-RG complexes deduced from the calculated potential curves are in quite reasonable agreement with available experimental data. In addition, the radial Schrodinger equation for nuclear motion was solved numerically with the calculated potentials to evaluate the corresponding vibrational levels and radial wavefunctions. The latter have been used in the calculation of the appropriate Franck-Condon factors to yield information on relative intensities of the vibrational bands of the Cd-RG complexes. The theoretical vibrational progressions are discussed in the context of experimental spectra.

Quasirelativistic valence ab initio calculation of the potential-energy curves for Cd-rare gas atom pairs

The results of large-scale valence ab initio calculations of the potential-energy curves for the ground states and several excited states of Cd–rare gas (RG) van der Waals molecules are reported. In the calculations, Cd20+ and RG8+ cores are simulated by energy-consistent pseudopotentials, which also account for scalar-relativistic effects and spin-orbit interaction within the valence shell. The potential energies of the Cd–RG species in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) calculations with a total 28 valence electrons, but the spin-orbit matrix has been computed in a reduced configuration interaction space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified spin-orbit matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the spectroscopic parameters derived for the ground states and several excited states of the Cd–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment.

Quasirelativistic valence ab initio calculation of the potential energy curves for the Hg–rare gas atom complexes

Results of large-scale valence ab initio calculations of potential energy curves for ground and several excited states of the Hg–rare gas (RG) van der Waals molecules are reported. In the calculations, the Hg 20+ and RG 8+ cores are simulated by energy-consistent pseudopotentials which also account for scalar-relativistic effects and spin–orbit (SO) interaction. Potential energies in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent field (CASSCF)/complete-active-space multireference second-order perturbation theory (CASPT2) calculations, while the SO matrix has been computed in a reduced CI space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified SO matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the derived spectroscopic parameters for the ground and several excited states of the Hg–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment.

Theoretical study of the electronic states of platinum trimer (Pt3)

Geometries and energy separations of various low-lying spin-states of the platinum trimer (Pt3) have been investigated. The complete active space multiconfiguration self-consistent field (CASMCSCF) method followed by large scale multiconfiguration singles plus doubles configuration interaction (MRSDCI) that included up to 4.26 million configuration spin functions were used to compute several electronic states. A relativistic configuration interaction (RCI) technique was employed to compute the spin-orbit effects in different electronic states. Although an equilateral triangular A11 state was found to be global minimum in the absence of spin-orbit effects, this state was found to be nearly degenerate with the B13(A1) spin-orbit state when spin-orbit coupling was included. The A11 and B13(A1) states were found to be heavily mixed by spin-orbit coupling. We also compared our MRSDCI results with the density functional as well as Møller–Plesset second order perturbation calculations. The dissociation and atomization energies have been computed and compared with experiment.

Theoretical study of electronic states of platinum pentamer (Pt5)

Geometries and energy separations of the various low-lying electronic states of Pt5 with different structural arrangements have been investigated. The complete active space multiconfiguration self-consistent-field (CASMCSCF) method followed by large-scale multiconfiguration singles plus doubles configuration interaction (MRSDCI) that included up to 1.64 million configuration spin functions have been used to compute several electronic states. A 1B2 (C2v) electronic state of a distorted tetragonal pyramid equilibrium structure was found to be the minimum energy geometry. We also compared our MRSDCI results with density functional as well as Mo/ller-Plesset second-order perturbation calculations. The dissociation and atomization energies have been computed and the results, together with our previous findings for the smaller Ptn (n=2–4) clusters, were compared with other group 10 member clusters viz., Nin (n=2–5) and Pdn (n=2–5) and the experimental findings.