Complete Active Space Multiconfiguration Self-consistent Field Research Articles

A b i n i t i o correlated valence shell effective Hamiltonian method for atomic and molecular systems

A new method for correlated electronic structure calculations that makes explicit reference to valence electrons only is presented for atomic and molecular processes in which the core electrons remain inert. The method is based on constructing a valence Hamiltonian that includes a one-electron effective potential for the core–valence interactions. It exactly reproduces all properties (wave functions, energies, etc.) of an all electron calculation with frozen core wave functions with same bases. It has no adjustable parameters, and no restrictions on the choice of basis sets. It yields considerable savings of computer time and space over the corresponding all electron calculations. Self-consistent field (SCF) and complete active space multiconfiguration self-consistent field (CAS-MCSCF) test calculations on ground states of F, F−, and S are presented.

Potential energy surfaces for insertion of hafnium atoms into hydrogen

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by second-order CI (SOCI) and relativistic CI (RCI) calculations including spin-orbit coupling are carried out on low-lying electronic states of HfH{sub 2}. Potential energy surfaces of 12 electronic states of HfH{sub 2} for studying the insertion of Hf(a{sup 3}F), Hf(a{sup 1}D), and Hf(a{sup 5}F) states into H{sub 2} are constructed. The authors find that the low-lying Hf({sup 1}D) inserts into H{sub 2} spontaneously to form the HfH{sub 2} molecule in the {sup 1}A{sub 1} state, while the {sup 3}F ground state of Hf atom has to surmount a barrier for insertion into H{sub 2}. However, the small but nonnegligible spin-orbit coupling matrix elements at the crossing of the {sup 1}A{sub 1} bent-structure surface with triplet surfaces provides a nonzero nonadiabatic transition probability for insertion of the Hf(a{sup 3}F) state with a smaller barrier into H{sub 2}. The {sup 1}A{sub 1} ground state of HfH{sub 2} was found to have r{sub e} = 1.842 {angstrom}, {theta}{sub e} = 126.7{degree}, {mu}{sub e} = 0.31 D, and D{sub e} = 30 kcal/mol relative to Hf({sup 3}F{sub 2}) + H{sub 2}. There are several low-lying triplet and singlet states that mix with each other in themore » presence of spin-orbit coupling.« less

Potential energy surfaces of LaH+ and LaH+2

Using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by full second-order configuration interaction (SOCI) calculations, 16 electronic states of LaH+ and 8 electronic states of LaH+2 are investigated. The potential energy surface of these electronic states of LaH+2 and LaH+ are computed. These calculations show that the 3F(5d2) ground state of La+ ion forms a weak complex with H2. The La+(1D) excited state inserts into H2 with a small barrier (<8 kcal/mol) to form the 1A1 ground state of LaH+2 (re=2.057 Å, θe=106°). At the SOCI level of theory LaH+2 is found to be 11 kcal/mol more stable than La+(3F)+H2. Our calculations explain the experimental observations on La++H2→LaH++H reaction. The adiabatic ionization potential (IP) of LaH2 and LaH are calculated as 5.23 and 5.33 eV, respectively. The ground state of LaH+ was found to be a 2Δ state. We compute De(LaH+) and De(HLa–H+) as 2.54 eV in excellent agreement with the experimental De(LaH+)=2.57 eV measured by Armentrout and co-workers. The spin–orbit effects of LaH+ were also studied using the relativistic configuration interaction (RCI) method.

Electronic states, ionization potentials, and bond energies of TlHn, InHn, TlH+n, and InH+n (n=1–3)

Potential energy surfaces of 6 electronic states of TlH2 and InH2 and 8 electronic states of TlH+2 and InH+2 are computed. In addition the ground states of TlH3, InH3, TlH+3, InH+3, TlH, and TlH+ are investigated. A complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by second-order configuration interaction (SOCI) and relativistic configuration interaction (RCI) including spin–orbit coupling calculations are carried out. The step-wise bond energies, De(Hn−1M–H) and adiabatic ionization potentials are computed. The ground states of TlH2 and InH2 are found to be bent (2A1; θe∼121.5 °, 120 °) while the ground states of TlH+2 and InH+2 are linear (1Σ+g). The ground states of TlH3 and InH3 are found to be 1A1 (D3h ) states while the ground states of TlH+3 and InH+3 are Jahn–Teller distorted 2B2(C2v ) states. The unique bond length of TlH+3 and InH+3 is shorter than the two equal bond lengths. The bond angles (H–M–H) for TlH+3 and InH+3 deviate considerably from the neutral θe=120 ° to near 69 °. The TlH+ ion is found to be only 0.04 eV stable. Periodic trends in the geometries, bond energies and IPs are studied. Spin–orbit effects were found to be significant for TlHn species. The IPs of InHn and TlHn exhibit odd–even alternation. The bond energies also show an interesting trend as a function of n.

Electron affinities of Ag 4 and Au 4

Electron affinities of Ag 4 and Au 4 as well as Ag 3 and Au 3 are computed using complete-active space multi-configuration self-consistent field (CAS MCSCF) followed by singles + doubles CI + Q (SDCI + Q) and multi-reference singles + doubles CI + Q (MRSDCI + Q) calculations which included up to 1.2 million configurations. Our computed electron affinities for the tetramers when scaled by a factor 1.3 and 1.35 for Ag 4 and Au 4, respectively, are in good agreement with the recent experimental values of Smalley and co-workers. The electron affinities of tetramers are found to be considerably smaller than trimers.

Potential energy surfaces for the Pt2+H2 reaction

Potential energy surfaces for the Pt2+H2 reaction are obtained using a complete active space multiconfiguration self-consistent field (CAS-MCSCF) method followed by multireference singles+double CI (MRSDCI) calculations. Several approaches of H2 such as parallel, perpendicular, collinear, end-on with respect to Pt2 are considered. In addition, out-of-plane twist motions of hydrogens relative to the Pt–Pt bond are considered. The parallel approach was found to be most reactive in the 1A1 electronic state, which forms a cis Pt2H2 saddle point after surmounting a barrier of ∼20 kcal/mol. The saddle point thus formed spontaneously transforms to a trans Pt2H2, 1Ag ground state through an out-of-plane twist motion. The dissociation of H2 in the parallel mode of collision was found to be brought about primarily through the interaction of the d(δ) orbitals of the two Pt atoms with the H2 1σg and 1σ*u orbitals. The spin–orbit effects were studied using a relativistic CI (RCI) method and found to be significant for Pt2H2. Spin–orbit coupling was found to induce an avoided crossing. This destabilizes the Pt2H2(1Ag) molecular state with respect to the dissociated Pt2+H2. The energy separation between the Pt2H2 1Ag trans minimum and the cis saddle point was calculated at the MRSDCI level as 3 kcal/mol. We find that the reactivity of Pt2 with H2 varies as a function of electronic state and orientation.

Electronic Structure and Properties of the O2+2, SO2+ and S2+2 Diatomic Dications

AbstractMultiply charged ions show novel energetic features which can potentially have useful photophysical properties. In order to investigate these interesting type systems, energy interaction curves for the ground and excited electronic states of O2+2, SO2+, and S2+2 have been generated by the ab initio complete active space multiconfiguration self‐consistent field (CAS‐MCSCF) method. The calculations were carried out in a triple‐zeta sp plus double‐zeta d Gaussian function basis set using compact effective potentials to replace the core electrons. In order to gauge the accuracy of the results, analogous calculations were carried out on the valence isoelectronic N2 and NO+ systems for which experimental information is available for comparison of geometric and spectroscopic properties. Diverse high energy spectroscopy experiments on O2+2 are interpreted and reconciled using the calculated ground and excited state energy interaction curves. Special attention is paid to the 3Σ+u state, whose location and character have been particularly puzzling. Almost all the dication molecular states studied show the characteristic avoided crossing of diabatic states which gives a trapped equilibrium structure and a barrier to dissociation. These features make the dication kinetically stable, but thermodynamically unstable with an exothermic dissociation energy. The spectroscopy experiments on O2+2 show that these states are experimentally attainable.

The low-lying states of the second-row transition metal hydrides (YH–CdH)

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by full second-order configuration interaction calculations which included up to 713 000 configurations are carried out on the low-lying states of all second-row transition metal hydrides (YH–CdH). A large (6s5p5d1f) valence Gaussian basis set together with relativistic effective core potentials which included the outer 4s24p64dn5s2 shells, were employed. The spectroscopic constants and potential energy curves of six electronic states of CdH are also obtained and compared with available experimental spectra. The ground states of YH, ZrH, NbH, MoH, TcH, RuH, RhH, PdH, AgH, and CdH were found to be 1∑+, 2Δ3/2, 3(I), 6∑+, 5∑+, 4∑−1/2, 3Δ, 2∑+, 1∑+, and 2∑+, respectively. For NbH, TcH, and RuH, 5Π, 7∑+, and 4Φ states, respectively, were found to be close to the ground states. The 5Π3 and 5Δ3 states of NbH undergo avoided crossing. The spectroscopic constants (re, μe, De, ωe, Te) of the low-lying states of these hydrides are computed and compared with available data on YH, RhH, PdH, and AgH. The theoretical re and ωe values are within 0.01 Å and 20 cm−1 of the experimental constants for these three hydrides.

Potential energy surfaces for Ir+H2 and Ir++H2 reactions

Potential energy surfaces of 10 electronic states of IrH2 and 12 electronic states of IrH+2 are computed. A complete active space multi-configuration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction (MRCI) calculations which included up to 270 000 configurations are employed. In addition spin–orbit effects are studied using the relativistic configuration interaction (RCI) method. It is found that the Ir(2F) state inserts spontaneously into H2 to form a stable IrH2 molecule in a 2A1 ground state which is 28 kcal/mol more stable than Ir(4F)+H2 in the absence of spin–orbit effects. The spin–orbit coupling of the quartet and doublet states provides nonzero transition probability for the insertion of Ir (4F) state into H2. The 3P state of Ir+ was found to insert spontaneously into H2 to form the 3A2 ground state of IrH+2 which is 30 kcal/mol more stable than Ir+(5D)+H2. An excited singlet state of Ir+ also was found to insert into H2 spontaneously. The spin–orbit couplings of quintet and triplet states of IrH+2 at the crossing of these curves provide nonzero transition probability for the insertion of Ir+ (5D) into H2. The bent E ground state of IrH2 in the C22v group was found to be a 63% 2A1, 16% 2B1 and 17% 2A2 mixture. This strong mixing induces a large H–Ir–H bond angle change of 9.5° in the E(III) state of IrH2. The 3A2 (A1) ground state of IrH+2 was found to be a 63% 3A2, 15% 3B2, 12% 3B1 and 7% 1A1 mixture. This strong spin–orbit mixing induces a θe change of almost 9° in the ground state of IrH+2. The adiabatic ionization potential including spin–orbit effects for IrH2 and Ir are calculated as 8.2 and 8.6 eV, respectively. The ground state of IrH2 was found to be ionic (μe=2.2 D) with Ir+H− polarity exhibiting Ir(6s0.756p0.125d8.06) hybridization. The IrH+2 ion in its 3A2 state exhibits Ir+(6s0.626p0.125d7.51) hybridization character.

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.

Potential energy surfaces of eight low-lying electronic states of Rh3

Complete active space multiconfiguration self-consistent-field (CASSCF) followed by multireference singles plus doubles configuration-interaction (MRSDCI) calculations which include 27 active electrons are carried out on eight low-lying electronic states of Rh3. The MRSDCI calculations included up to 2.3 million configurations. The spin-orbit effects are included by using the relativistic configuration-interaction (RCI) method. All the low-lying states considered here lie within 0.20 eV. All the doublet states are Jahn–Teller components of the doubly degenerate 2E′ and 2E″ states in equilateral triangular geometry (D3h), while the quartet states arise from the Jahn–Teller components of 4E′ and 4E″ states. The splittings between the two Jahn–Teller components of both the 2E′ and 2E″ states, which yield barriers to pseudorotation, are 3.9 kcal/mol. The lowest-lying 2A2 and 2A1 states are separated only by 0.03 eV. Thus, low-lying electronic states of Rh3 are best described using a dynamic Jahn–Teller model. The Mulliken population analyses of the MRSDCI natural orbitals reveal the larger s population of the apex atom of the isosceles triangle in comparison to the base atoms. The base atoms have larger d populations for all electronic states. The present calculations also reveal a considerable mixing among the 4d85s1, 4d9, and 4d85p1 configurations of the rhodium atom. The atomization energy of Rh3 is calculated as 188 kcal/mol. The trimer (Rh3) is predicted to be considerably more stable than the dimer (Rh2).

Electronic states and potential energy surfaces of H2Te, H2Po, and their positive ions

Geometries, bond energies, ionization potentials, dipole moments, other one-electron properties, and potential energy surfaces of six valence electronic states of H2Te and H2Po species are obtained using the relativistic complete active space multiconfiguration self-consistent field (CASSCF) followed by full second-order configuration interaction (SOCI) and relativistic configuration interaction (RCI) calculations including spin–orbit coupling. In addition, Rydberg states of H2Te and H2Se are studied to interpret the experimental spectra. The potential energy surfaces of two electronic states of H2Te+ and H2Po+ are obtained. The ground states of both H2Te and H2Po are found to be of X 1A1(A1) symmetry with bent (C2v) equilibrium geometries of H2Te:re=1.668 Å, θe=91.2°; and H2Po:re=1.835 Å and θe=90.9°. The ground states of H2Te+ and H2Po+ are X 2B1 with H2Te+:re=1.676 Å, θe=90.7° and H2Po+:re=1.828 Å and θe=88°. The De (HTe–H) and De (HPo–H) including spin–orbit effects are calculated as 63.2 and 39.4 kcal/mol, respectively. The X 2B1(E)−A 2A1(E) energy separations of H2Te+ and H2Po+ ions are calculated as 66.6 and 76 kcal/mol, respectively. The adiabatic IPs of H2Te and H2Po are calculated as 8.47 and 7.79 eV, respectively. In addition CASSCF/SOCI/RCI calculations are also carried out on the X 2Π3/2 and 2Π1/2 states of TeH and PoH diatomics. The X 2Π3/2–2Π1/2 energy separations of TeH and PoH are computed as 3710 and 9920 cm−1, respectively. Spin–orbit effects are thus found to be very significant for PoH and H2Po. All excited states of H2Te and H2Po are above 3.7 and 3.1 eV, respectively. Properties and energy separations of H2Te and H2Po are compared with the lighter group (VI) H2Ch species.

Relativistic CASSCF/CI calculations: Applications to transition metal dihydrides

A complete active space MCSCF (multi-configuration self-consistent field) scheme (CASSCF) using relativistic effective potentials followed by configuration interaction and relativistic CI calculations provides a very good description of the electronic states and potential energy surfaces of transition metal dihydrides. Such calculations are of considerable value not only in our understanding of the transition metal-hydrogen bonding but also in the prediction of the barrier to insert the metal atom into the H2 bond. All-electron CASSCF/CI calculations are carried out on twelve electronic states of CoH2. Comparable RECPCASSCF/CI calculations are also carried out to show that the RECP-CASSCF/CI calculations provide an accurate method for the investigation of transition metal compounds. The general method of RECP-CASSCF/CI Calculations for molecules containing heavy atoms is described. The calculations on CoH2 are compared with similar calculations on ScH,, YH2, FW2, and PdH2. A critical comparison of all these transition metal hydrides reveals that in general the low-spin excited metal atom inserts into H2 spontaneously while the high spin ground state atom has to surmount a large barrier.

Electronic states and potential energy surfaces of gold dihydride

Complete active space multiconfiguration self-consistent field (CASSCF) followed by second-order configuration interaction (SOCI) calculations as well as multireference singles and doubles CI (d-MRSDCI) including the d electrons of Au are carried out on the two low-lying electronic states (/sup 2/B/sub 2/ and /sup 2/A/sub 1/) of AuH/sub 2/. The bending potential energy surfaces of the /sup 2/B/sub 2/ and /sup 2/A/sub 1/ states with the bond lengths optimized for all angles are presented. The ground state of AuH/sub 2/ is found to be a bent /sup 2/B/sub 2/ electronic state with a bending angle of 127/sup 0/ at the d-MRSDCI level and 128/sup 0/ at the CASSCF/SOCI level. The d correlation is shown to be significant, especially for the /sup 2/B/sub 2/ (bent) state. Two linear states, namely /sup 2/..sigma../sub g//sup +/ and /sup 2/..sigma../sub u//sup +/, approximately 0.88 and 0.59 eV, respectively, above the /sup 2/B/sub 2/ bent ground state are found. The bending potential energy surfaces of the two states reveal that the ground state of the gold atom (/sup 2/S) has to surmount a large barrier (90 kcal/mol) to insert into H/sub 2/ to form the /sup 2/..sigma../sub g//sup +/ linear state while the excited /sup 2/Pmore » state of the gold atom inserts spontaneously into H/sub 2/ to form the bent /sup 2/B/sub 2/ ground state. The AuH/sub 2/ ground state is about 0.85 eV less stable than Au(/sup 2/S) + H/sub 2/ at the d-MRSDCI level while the atomization energy of AuH/sub 2/ (i.e., AuH/sub 2/(/sup 2/B/sub 2/) ..-->.. Au(/sup 2/S) + 2H) is found to be 3.71 eV.« less