Calculation of molecular electronic spectra by projected-unrestricted Hartree–Fock theory

This paper is concerned with a new application of projected-unrestricted Hartree–Fock theory, namely, the calculation of electronic spectra for symmetric molecules. The excited electronic state is represented by a single determinant whose unrestricted nature allows for orbital rearrangement relative to the self-consistent ground state. The self-consistent calculation must be followed by spin projection to obtain appropriate spin eigenstates. It was necessary to develop modified procedures for portions of the spin projection calculation because our method of constructing the wave functions produces degeneracies among the natural orbitals. Illustrative calculations using the all-valence-electron INDO approximations produced results which compared favorably with configuration-interaction treatments. The method described here should be most useful, however, in conjunction with ab initio calculations using flexible basis sets.     

Iterative Cl general singles and doubles (ICIGSD) method for calculating the exact wave functions of the ground and excited states of molecules

The iterative configuration-interaction general singles and doubles (ICIGSD) method was applied to various closed- and open-shell electronic states of molecules within finite basis sets and was shown to give the exact results that are identical to the full CI ones. The structure of the ICIGSD is unique among the ICI formalisms, that is, the singularity problem intrinsic to atomic and molecular Hamiltonians can be avoided. The convergence of the ICIGSD method was fairly good regardless of the characters of the electronic states and the qualities of the basis sets; only several iterations were enough for obtaining microhartree accuracy. These favorable properties are attributed to the unique GSD structure. The present method was shown to be applicable to various spin states and to quasidegenerate states appearing in bond dissociation process. We have also applied the ICIGSD-CI method to calculate the excited states simultaneously. We have confirmed that the ICIGSD-CI method is accurate for calculating the excited states the symmetries of which are not only similar to but also different from that of the ground state.     

Pseudopotential investigation of some alkali metal molecules

The effect of electron correlation on the results of pseudopotential calculations was examined using a simple analytical semiempirical pseudopotential and a correlated floating-type one-center wave function. Investigations were performed for the XH alkali metal hydride molecules (X ? Na, K, Rb, Cs). The inclusion of the electron correlation in the ground state proved important for the calculation of the dissociation and ionization energies, but it is less significant for the determination of the equilibrium nuclear distances. The ground state potential energy curves are also determined.     

Performance of the general-model-space state-universal coupled-cluster method

The capabilities of the recently developed multireference, general-model-space (GMS), state-universal (SU) coupled-cluster (CC) method have been extended in order to enable the handling of any excited state that represents a single (S) or a double (D) excitation relative to the ground state. A series of calculations concerning the ground and excited states of the CH(+), HF, F(2), H(2)O, NH(2), and CH(2) molecules were carried out so as to assess the performance of the GMS SU CCSD method. For diatomics we have computed the entire potential energy curves, while for triatomics we have focused on vertical excitation energies. We demonstrate how a systematic enlargement of the model space enables a consideration of a larger and larger number of excited states. A comparison of the CC and full configuration interaction or large-scale CI results enables an assessment of the accuracy and reliability of the GMS SU CCSD method within a given basis set. In all cases very good results have been obtained, including highly excited states and those having a doubly-excited character.     

Ab initio study of the electronic structure of manganese carbide

We report electronic structure calculations on 13 states of the experimentally unknown manganese carbide (MnC) using standard multireference configuration interaction (MRCI) methods coupled with high quality basis sets. For all states considered we have constructed full potential energy curves and calculated zero point energies. The X state, correlating to ground state atoms, is of 4sigma- symmetry featuring three bonds, with a recommended dissociation energy of D0 = 70.0 kcal/mol and r(e) = 1.640 angstroms. The first and second excited states, which also correlate to ground state atoms, are of 6sigma- and 8sigma- symmetry, respectively, and lie 17.7 and 28.2 kcal/mol above the X state at the MRCI level of theory.     

Theoretical characterization of the low-lying electronic states of NbC

We have studied the potential-energy curves and the spectroscopic constants of the ground and low-lying excited states of NbC by employing the complete active space self-consistent field method with relativistic effective core potentials followed by multireference configuration-interaction calculations. We have identified 23 low-lying electronic states of NbC with different spin multiplicities and spatial symmetries within 40,000 cm(-1). At the multireference single and double configuration interaction level of theory the 2sigma+ and 2delta states are nearly degenerated, with the 2delta state located 187 cm(-1) lower than the 2sigma+ state. The estimated spin-orbit splitting for the 2delta state results in a 2delta(3/2) ground state and A 2sigma+ which is placed 650 cm(-1) above the ground state, in reasonable agreement with the experimental result, 831 cm(-1). Our computed spectroscopic constants are in good agreement with experimental values although our results differ from those of a previous density-functional investigation of the excited states of NbC, mainly due to the strong multiconfigurational character of NbC. In the present work we have not only suggested assignments for the observed states but also computed more electronic states that are yet to be observed experimentally.     

Sources of error in electronic structure calculations on small chemical systems

The sources of error in electronic structure calculations arising from the truncation of the one-particle and n-particle expansions are examined with very large correlation consistent basis sets, in some cases up through valence 10-zeta quality, and coupled cluster methods, up through connected quadruple excitations. A limited number of full configuration interaction corrections are also considered. For cases where full configuration interaction calculations were unavailable or prohibitively expensive, a continued fraction approximation was used. In addition, errors arising from corevalence and relativistic corrections are also probed for a number of small chemical systems. The accuracies of several formulas for estimating total energies and atomization energies in the complete basis set limit are compared in light of the present large basis set findings. In agreement with previous work, the CCSD(T) method is found to provide results that are closer to the CCSDTQ and full configuration-interaction results than the less approximate CCSDT method.     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.     

Broadband Vibrational Cooling of Cold Cesium Molecules： Theory and Experiments

The use of a broadband, frequency shaped femtosecond laser on translationally cold cesium molecules has recently demonstrated to be a very efficient method of cooling also the vibrational degree of freedom. A sample of cold molecules, initially distributed over several vibrational levels, has thus been transfered into a single selected vibrational level of the singlet X^1∑g ground electronic state. Our method is based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but limited in its frequency bandwidth with a spatial light modulator. In such a way we are able to eliminate transitions from the selected level, in which molecules accumulate. In this paper we briefly report the main experimental results and then address, in a detailed way by computer simulations, the perspectives for a ＂complete＂ cooling of the molecules, including also the rotational degree of freedom. Since the pumping process strongly depends on the relative shape of the ground and excited potential curves, ro-vibrational cooling through different excited states is theoretically compared.     

Ab initio relativistic calculation of the RbCs molecule

We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.     

Evidence for excited spin-orbit state reaction dynamics in F+H2: theory and experiment

We describe fully quantum, time-independent scattering calculations of the F+H2-->HF+H reaction, concentrating on the HF product rotational distributions in v'=3. The calculations involved two new sets of ab initio potential energy surfaces, based on large basis set, multireference configuration-interaction calculations, which are further scaled to reproduce the experimental exoergicity of the reaction. In addition, the spin-orbit, Coriolis, and electrostatic couplings between the three quasidiabatic F+H2 electronic states are included. The calculated integral cross sections are compared with the results of molecular beam experiments. At low collision energies, a significant fraction of the reaction is due to Born-Oppenheimer forbidden, but energetically allowed reaction of F in its excited (2P 1/2) spin-orbit state. As the collision energy increases, the Born-Oppenheimer allowed reaction of F in its ground (2P 3/2) spin-orbit state rapidly dominates. Overall, the calculations agree reasonably well with the experiment, although there remains some disagreement with respect to the degree of rotational excitation of the HF(v'=3) products as well as with the energy dependence of the reactive cross sections at the lowest collision energies.     

Biradicals stabilized by intramolecular charge transfer: properties of heterosubstituted pentalene and cyclooctatetraene biradicals

Intramolecular charge transfer can lead to substantial stabilization of singlet ground state and a corresponding increase of the singlet-triplet gap for molecules isoelectronic with the dianions of antiaromatic hydrocarbons. The formal biradicals 2,5-di-heterosubstituted-pentalenes and 1,5-di-heterosubstituted-cyclooctatetraenes are theoretically predicted to have the potential to be stable, persistent non-Kekulé molecules, as supported by high-level quantum chemical calculations. The singlet-triplet energy gaps and the S(0)-S(1) excitation energies of these molecules are similar to those of aromatic molecules rather than standard biradicals. These formal biradicals have a pronounced zwitterionic character, having a singlet ground state. The marked stabilization of the ground-state singlet for these non-Kekulé molecules is accompanied by a significant destabilization of the highest occupied molecular orbital (HOMO), leading to a low ionization potential (IP). This apparent inconsistency is explained by analyzing the electronic structure of the molecules. In the case of di-aza-pentalene, the energy of the first electronic excited state is only slightly lower than the ionization potential, making it a candidate for molecular autoionization.     

Generation of potential energy curves for the X1Sigma(+)g, B1Delta(+)g, and B'1Sigma(+)g states of C2 using the effective valence shell Hamiltonian method

Calculations of the ground and excited state potential energy curves of C2 using the third-order effective valence Hamiltonian (Hv3rd) method are benchmarked against full configuration interaction and other correlated single-reference perturbative and nonperturbative theories. The large nonparallelity errors (NPEs) exhibited even by state-of-art coupled cluster calculations through perturbative triples indicate a serious deficiency of these single-reference theories. The Hv method, on the other hand, produces a much reduced NPE, rendering it a viable approximate many-body method for accurately determining global ground and excited state potential energy curvessurfaces.     

乙基硫自由基及阴、阳离子低电子激发态从头算研究

采用CASSCF方法和6-311++(3df, 3pd)基组以及Cs对称性优化了乙基硫自由基和阳、阴离子3种分子的12个电子态的几何构型. 利用二级微扰方法(CASPT2)对这12个电子态做了单点能校正. 通过比较自由基与阴阳离子的能量, 得出了绝热电子亲和势和绝热电子电离能, 与实验结果在允许误差范围内基本一致.     

Relativistic calculations of AuSi+ and AuSi−

Theoretical calculations of the electronic structure of the ground state and a series of excited states of the AuSi⁺ and AuSi⁻ molecules are presented. The calculations were carried out with the spin-free relativistic infinite-order two-component (IOTC) method and high-level complete active space self-consistent field/complete active space perturbation theory correlated methods. The spin-orbit (SO) coupling was introduced via the restricted active space state interaction method with the use of the atomic mean-field SO integrals. The work presents the spectroscopic parameters of calculated states and full potential energy curves of the ionic AuSi⁺ and AuSi⁻ structures for the first time. Electrostatic potential maps projected on the electron density surface illustrate the significant relativistic effects on going from nonrelativistic to scalar relativistic treatments.     

Ab initio configuration-interaction study of the ground and low-lying electronic states of NiI

For the first time, we have studied the potential-energy curves, spectroscopic terms, vibrational levels, and the spectroscopic constants of the ground and low-lying excited states of NiI by employing the complete active space self-consistent-field method with relativistic effective core potentials followed by multireference configuration-interaction calculations. We have identified six low-lying electronic states of NiI with doublet spin multiplicities, including three states of Delta symmetry and three states of Pi symmetry of the molecule within 15 000 cm(-1). The lowest (2)Delta state is identified as the ground state of NiI, and the lowest (2)Pi state is found at 2174.56 cm(-1) above it. These results fully support the previous conclusion of the observed spectra although our computational energy separation of the two states is obviously larger than that of the experimental values. The present calculations show that the low-lying excited states [13.9] (2)Pi and [14.6] (2)Delta are 3 (2)Pi and 3 (2)Delta electronic states of NiI, respectively. Our computed spectroscopic terms, vibrational levels, and spectroscopic constants for them are in good agreement with the experimental data available at present. In the present work we have not only suggested assignments for the observed states but also computed more electronic states that are yet to be observed experimentally.     

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.