Complete Active Space Multiconfiguration Self-consistent Field Research Articles

Electronic structures of Pd4 and Pt4

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction computations which included up to 4.1 million configurations and correlated all 40 electrons of Pd4 and Pt4 were made. Relativistic effective core potentials (RECPS) were employed for both Pt and Pd atoms. We found 44 electronic states for Pd4 within the 2.2 eV region and 51 electronic states for Pt4 within 1.2 eV. Two nearly-degenerate electronic states with tetrahedral geometries were found as candidates for the ground states of Pd4 and Pt4 with 3T1 and 1A1 symmetries at the highest level of theory. The metal–metal bond lengths for Pd4 and Pt4 were found to be 2.686 and 2.602 Å for the 3T1 state and 2.696 and 2.595 Å for the 1A1 state, respectively. The atomization energies of Pd4 and Pt4 were computed as 5.63 and 11.8 eV, respectively, suggesting that Pt4 is considerably more bound compared to Pd4. Relativistic effects are attributed to the enhanced stability of Pt4. The Mulliken population analysis reveals enhanced Pt(6s) and reduced Pt(5d) populations for the electronic states of Pt4 while the electronic states of Pd4 exhibit the opposite trend.

Electronic states of the Ga 3As 2 and Ga 2As 3 clusters

We computed the optimized geometries and energy separations of several electronic states of Ga 3As 2 and Ga 2As 3 clusters using the complete active space multiconfiguration self-consistent-field (CASSCF) followed by multireference singles + doubles configuration interaction (MRSDCI) computations which included up to 1.9 million configurations. The properties of the electronic states in distorted and undistorted trigonal bipyramid, and edge-capped tetrahedron structures of Ga 3As 2 are computed. Two nearly degenerate structures and several excited states were found for Ga 3As 2 while the Ga 2As 3 cluster exhibits undistorted trigonal bipyramidal states.

Full Configuration Interaction Molecular Dynamics of Na2 and Na3

We extend our ab initio molecular dynamics methods to more exact wave functions, including complete active space multiconfiguration self-consistent-field (CASSCF) and full configuration interaction (full CI) wave functions. These extensions are critical for describing properly the dynamics of bond formation/ dissociation and isomerization, as we illustrate here by examining the bond dissociatiordformation of Naz and the isomerization (“pseudorotation”) of Na3 with full CI dynamics. Equivalencing of all three atoms of Na3 is found to proceedfirst via facile inversions through linear structures, which occur more often than conventional pseudorotation (via obtuse to acute to obtuse isosceles triangles).

Twelve electronic states and potential energy surface of Zr 3

We compute the properties of twelve electronic states (of singlet, triplet and quintet spin multiplicities) of zr 3 using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) method followed by multireference singles + doubles configuration interaction (MRSDCI) calculations. We find two nearly degenerate states ( 1A 1, 3B 1) as candidates for the ground state of Zr 3 at the MRSDCI level. The 1A 1 state exhibits a double minimum due to an avoided crossing.

Spectroscopic Properties and Potential Energy Curves for 21 Electronic States of CrH

Spectroscopic constants and potential energy curves of 21 electronic states of CrH are obtained using the all-electron complete active space multiconfiguration self-consistent field (CASMCSCF) followed by first-order configuration interaction (FOCI) and full second-order CI (SOCI) and multireference CI including Rydberg states calculations. The ground state of CrH is found to be of 6Σ+ symmetry with re = 1.690 Å, ωe = 1592 cm−1, De = 2.11 eV, and μe = 3.864 D at the SOCI level. Several optical transitions for CrH are predicted. Our computations support the reassignment of the state perturbing the A-X system to 4Σ+ suggested by Ram et al. Our computed spectroscopic constants for the A, X, and a 4Σ+ state are in excellent agreement with the experimental values reported by Ram et al.

Germanium monochloride (GeCl). Spectroscopic constants and potential energy curves

The electronic states, potential energy curves and spectroscopic properties of the GeCl radical were calculated by means of the relativistic ab initio complete active space multiconfiguration self-consistent field (CASSCF) followed by first- and second-order configuration interaction (FOCI, SOCI) methods which included up to a million configurations. Our computed spectroscopic constants are in good agreement with the experiment for the observed states. Spectroscopic constants and potential energy curves of several other electronic states are computed which are yet to be observed. We also show that a previous rotational analysis of the B—X system is incorrect.

First-principle interatomic potentials for the carbon monoxide—platinum reaction

A general method for generating atom3ātom potentials, which reproduce ab initio potential curves for some geometrical rearrangements, is presented. Pairwise potentials are derived from reliable large scale complete active space multi-configuration self-consistent field (CASSCF) calculations. The reaction of carbon monoxide with a plantinum atom has been selected as a test case. The interaction energies calculated from these atom—atom potentials are compared with our ab initio CASSCF calculations including many-body effects.

Geometries and potential energies of electronic states of GaX2 and GaX3 (X=Cl, Br, and I)

Twelve electronic states of GaCl2, GaBr2, and GaI2 and the 1A1′ electronic states of GaCl3, GaBr3, and GaI3 are investigated using the complete active space multiconfiguration self-consistent-field (CAS-MCSCF) technique which included up to 58 700 configurations followed by multireference singles+doubles configuration interaction (MRSDCI) method which included a larger configuration space. Potential energy surfaces of four doublet electronic states of GaCl2, GaBr2, and GaI2 are obtained. Seven excited electronic states of GaBr3 are also studied. The ground states of GaX2 (X=Cl, Br, and I) species are found to be of X 2A1 symmetries (C2v), while the ground states of GaX3 species are found to be of X 1A1′ symmetries (D3h). The potential energy surfaces of the excited 2B1 states of GaX2 compounds exhibit double minima. The dissociation energies and the atomization energies of GaX2 and GaX3 are computed.

Energy separations for the electronic states of PH −2,PH 2 and PH +2

All-electron complete-active space multi-configuration self-consistent field (CASSCF) followed by second-order configuration interaction (SOCI) calculations in conjunction with large P(13s10p3d2flg/7s6p3d2flg) and H (10s5p1d/8s5p1d) basis sets are made on the electronic states of PH − 2, PH 2 and PH + 2. We compute the adiabatic electron affinities of PH 2 and PH. The 3B 1−X 1A 1, 1B 1−X 1A 1 energy separations of PH + 2 and the 2A 1−X 2B 1 energy separation of PH 2 are computed.

Electronic structure of the group V tetramers (P4–Bi4)

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction (MRCI) and relativistic configuration interaction (RCI) calculations, which included up to 2 million configurations, are carried out on the ground and excited states of P4–Bi4. We computed the properties of the 1A1 ground state with tetrahedral geometry as well as five excited states of triplet, singlet, and quintet multiplicities of these clusters. The computed results were used to assign the negative photodetachment spectra of Sb4− and Bi4− as well as the matrix isolated spectra of small Bi clusters. We found spin–orbit effects were quite large for Bi4. Our computations are consistent with the recent reassignment of the spectra of Bi4 observed by Bondybey and English to Bi3.

Spectroscopic constants and potential energy curves for 18 electronic states of IrH +

Spectroscopic constants and potential energy curves of 18 electronic states of IrH + are obtained using the complete active space multi-configuration self-consistent field (CASMCSCF) followed by first-order configuration interaction (FOCI) and multi-reference singles + doubles CI (MRSDCI) calculations. The spin-orbit effects are introduced using the relativistic-configuration-interaction (RCI) method. The ground state of IrH + is found to be of 4Σ − symmetry with r e = 1.548 A ̊ , ω e = 2296 cm −1, and D e = 3.28 eV in the absence of spin-orbit interactions, while three nearly degenerate states [ 1 2 ( I) , 1 2 ( II) , 9 2 ( I) ] are found as candidates for the ground state including spin-orbit coupling. Several optical transitions for IrH + are predicted, none of which has been observed experimentally. The nature and bonding of the low-lying electronic states are analyzed.

Potential energy surfaces for Pd2+H and Ni2+H interactions

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference singles+doubles configuration interaction (MRSDCI) calculations are carried out for Pd2+H and Ni2+H interactions. Spin–orbit effects are also included through the relativistic configuration interaction (RCI) method for Pd2H. We find that both Ni2H and Pd2H form M MH (M=Pd,Ni) bridge equilibrium structures. Three nearly-degenerate electronic states are found for both Pd2H and Ni2H. The nature of the metal hydrogen bridge bonds is discussed. For Pd2H the spin–orbit contamination of nearly-degenerate low-lying states was found to be significant.

Potential energy surfaces for OsH2

We compute the potential energy surfaces of 12 electronic states of OsH2 (four quintet, four triplet, and four singlet) arising from5D ground state of the Os atom as well as triplet and singlet excited states using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction (MRCI) and relativistic CI (RCI) calculation which include up to 430,000 configurations. We find that the5D ground state of Os atom does not insert into H2 while the excited3F state of Os does. The3B1 ground state of OsH2 (there are two other nearly degenerate states) in the absence of spin-orbit coupling was found to be 22 kcal/mol more stable than Os(5D)+H2. The spin-orbit mixing of3B1,3B2,3A2, and1A1 states was so strong that it induces significant change in bond angles (up to 10°) for OsH2.

Excited electronic states of Au 3

Complete active space multi-configuration self-consistent field (CASSCF), followed by multi-reference configuration interaction (MRSDCI) calculations, which correlated 33 outer electrons of Au 3 were made of fifteen electronic states of Au 3. Spin—orbit effects were also included using the relativistic configuration interaction method. Our calculations facilitate tentative assignment of six peaks in the UPS spectrum of Au − 3 obtained by Smalley and co-workers.

Potential energy surfaces for the insertion of Ta and Ta+ into H2

We compute the bending potential energy surfaces of 12 electronic states of TaH2 and TaH+2 using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference singles+doubles configuration interaction (MRSDCI) calculations. Spin–orbit effects are also included using the relativistic configuration interaction (RCI) approach. We find that the 4F ground state of Ta atom requires a barrier of ∼24 kcal/mol for insertion into H2 while the 5F ground state of Ta+ does not insert into H2. The low-spin excited states of Ta and Ta+ are considerably more reactive with H2. We find three nearly-degenerate bent electronic states of 4B1, 4A2, and 4B2 symmetries as the candidates for the ground state of TaH2. Likewise 3B1 and 3A1 electronic states of TaH+2 are nearly-degenerate candidates for the ground state. The spin–orbit coupling strongly mixes some of these states leading to bond angle changes of up to 10°.

Potential energy surfaces for the insertion of Re and Re+ into H2

Potential energy surfaces of 12 electronic states of ReH2 and 13 electronic states of ReH+2 are computed. Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction calculations, which included up to 1.5 million configurations, were carried out on these electronic states of ReH2 and ReH+2. In addition, spin-orbit effects were included using the relativistic configuration interaction (RCI) method. Our computations reveal that the ground states of Re(6S) and Re+(7S) do not insert into H2 while the excited Re(6D) and Re+(5G) states insert into H2 spontaneously. The ground state of ReH2 is found to be a high-spin linear 6Σ+g state while the ground state of ReH+2 is found to be a bent 5B2 state. There are low-lying bent sextet and quartet minima for ReH2 while there are corresponding triplet and singlet bent minima for ReH+2. The 3B2 and 1B2 bending potential energy surfaces of ReH+2 exhibit double minima attributed to two possible Re(d) hybridizations. The spin-orbit effects were found to be non-negligible for both ReH2 and ReH+2.

Geometry and electronic structure studies using computational quantum chemistry

Some very recent applications in ab initio computational quantum chemistry are reviewed and mainly previewed. A large number of sulphone, sulphoxide and sulphide geometric structures have been gradient optimized at the single electronic configuration self-consistent field (SCF) level using a 6-31G ∗ (or 6-31+G ∗ for anions) basis set. This collection allows a comparison and understanding of trends and effects in their electronic and geometric structural properties. The degree of intra- and inter-molecular hydrogen bonding involving the methyl group with the SO bond in hypervalent sulphur compounds has been characterized. A comparison of calculated dimer and 1:1 monomer-water complex structures allows a consideration of the relative importance of different hydrogen bonding situations (C-H, S-H and O-H with the SO bond) in these types of compound. A number of other hydrogen-bonded adducts involving (C-)H-O(C) and (HO-)H&-O(P) interactions, which shed light on recent experimental results, have also been studied. The homonuclear and mixed triple-bonded diatomic molecules (XY n+ ) with X, Y = nitrogen and oxygen form a ten-valent electron isoelectronic series (N 2, NO + and O 2 2+) for comparison of calculated properties with experiment. The O 2 2+ energy interaction curve shows an interesting avoided curve crossing and a metastable energy minimum, a barrier to dissociation and an exothermic bond energy. For these systems, the complete active space multi-configuration SCF method is needed for even a qualitatively correct electronic structure description of the whole curve. Relativistic effective core potentials, which replace the inert core electrons in the heavier elements, allow this study to be extended to, for example, Pt 2 2+, Au 2 2+ and Hg 2 2+, as well as the whole XY 2+ series with X, Y = O, S, Se and Te.

Spectroscopic constants and potential energy curves of Bi2 and Bi−2

We compute the spectroscopic constants of 26 electronic states of Bi2 and six electronic states of Bi−2. In addition, the potential energy curves of electronic states of Bi2 dissociating into Bi(4S)+Bi(4S), Bi(4S)+Bi(2D), Bi(4S)+Bi(2P), Bi(2D)+Bi(2D), and Bi(4S)+Bi(4P) limits are computed. We use a complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by first-order configuration interaction (FOCI) and second-order configuration interaction (SOCI) methods. In addition, the spin–orbit effects are included through the relativistic configuration interaction (RCI) method. Our computed spectroscopic properties facilitate the assignment of recently observed negative ion photodetachment spectra as well as the electronic spectra accumulated up to now. The observed lifetime and transition moment dependence on internuclear distance are also explained based on computed potential energy curves.

Spectroscopic constants and potential energy curves for TaH

Spectroscopic constants and potential energy curves of 21 electronic states of the diatomic TaH are computed using complete active space multiconfiguration self-consistent field (CASSCF) followed by second-order configuration interaction (SOCI) calculations. In addition spin-orbit effects were included using the relativistic configuration interaction method (RCI). The ground state of TaH was found to be a 0 + state, which is a mixture of 5Δ(0 +), 5Π(0 +), 3Σ −(0 +), and 3Π(0 +). The spin-orbit effects were found to be significant for TaH. Several spectroscopic transitions are predicted for TaH none of which is observed.

Group V trimers and their positive ions: The electronic structure and potential energy surfaces

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interactions (MRCI) calculations are made on the electronic states of P3, As3, Sb3, Bi3 and all their positive ions. All group V trimers have Jahn-Teller distorted 2A2 ground states arising from the 2E″(D3h) state while the positive ions have 1A′1(D3h) equilateral-triangular ground states. For the neutral species, the 2B1 Jahn-Teller component was found to be nearly degenerate with the 2A2 component. Extensive studies on As3, Sb3, and Bi3 reveal the existence of 4A2, 4E′, and 2E′ (D3h) excited states which also undergo Jahn-Teller distortion. The binding energies and the ionization potentials (IP) of all group V trimers were computed and compared with known experimental data on some of these species. The IPs and the binding energies per atom of group V trimers were found to be significantly smaller than dimers thus exhibiting odd–even alternation in these properties. Our computations explain the dramatically different photofragmentation patterns for antimony and bismuth clusters observed by Geusic et al.