State Potential Energy Curves Research Articles

Modeling the adiabatic connection in H2

Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of H2, within spin-restricted density functional theory (DFT). For each internuclear separation R, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate R, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all R, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.

Investigating excited electronic states ofI2+andI22+produced by strong-field ionization using vibrational wave packets

In pump-probe experiments with a femtosecond near-uv laser, a wave packet is launched onto an excited electronic state of I{sub 2}{sup +} through strong field ionization, and starts vibrating in the corresponding potential well. The vibrational wave packet is further ionized by a probe pulse to an excited electronic state of I{sub 2}{sup 2+} that dissociates into I{sup 2+}+I{sup 0+}. Projecting the vibrational wave packet onto the dissociation channel reveals characteristics of both potential curves via the periodic variations in kinetic energy distribution of the dissociating fragments. The experimental results are consistent with theoretical simulations that are sensitive to the shape of the potential curves. We find that the intermediate state in I{sub 2}{sup +} is A{sup 2}{pi}{sub u,3}/{sub 2} and ionization to this state has an anomalous angular dependence. Moreover, we extract the I{sup 2+}+I{sup 0+} potential energy curve and find evidence for a truly bound potential well, in contrast to the metastable ground state potential energy curves.

State-specific multireference complete-active-space coupled-cluster approach versus other quantum chemical methods: dissociation of the N2 molecule

A comprehensive comparison of different quantum-chemical methods applied to calculate the N2 ground state potential energy curve is presented. In the comparison we highlight the multireference state-specific (MRSS) coupled-cluster (CC) approach with the complete-active-space (CAS) reference and with single and double excitations from all reference determinants in the CC operator developed in our group. The method is called CASCCSD. The energy and amplitude equations for the method and the corresponding computer code have been generated using a computerized automative procedure that in the present work was extended to produce a parallel computer code. The complete CASCCSD wave function for N2 includes some selected eight-fold excitations in the CC operator. An analysis of the wave function estimates the importance of those excitations at large internuclear separations.

Electronic States and Spectroscopic Properties of SiTe and SiTe+

Ab initio based configuration interaction calculations have been carried out to study the low-lying electronic states and spectroscopic properties of the heaviest nonradioactive silicon chalcogenide molecule and its monopositive ion. Spectroscopic constants and potential energy curves of states of both SiTe and SiTe+ within 5 eV are reported. The calculated dissociation energies of SiTe and SiTe+ are 4.41 and 3.52 eV, respectively. Effects of the spin-orbit coupling on the electronic spectrum of both the species are studied in detail. The spin-orbit splitting between the two components of the ground state of SiTe+ is estimated to be 1880 cm(-1). Transitions such as 0+ (II)-X1Sigma(+)0+, 0+ (III)-X1Sigma(+)0+, E1Sigma(+)0+ -X1Sigma(+)0+, and A1Pi1-X1Sigma(+)0+ are predicted to be strong in SiTe. The radiative lifetime of the A1Pi state is less than a microsecond. The X(2)2Pi(1/2)-X(1)2Pi(3/2) transition in SiTe+ is allowed due to spin-orbit mixing. However, it is weak in intensity with a partial lifetime for the X2 state of about 108 ms. The electric dipole moments of both SiTe and SiTe+ in their low-lying states are calculated. The vertical ionization energies for the ionization of the ground-state SiTe to different ionic states are also reported.

Photodissociation of Mg+–XCH3 (X=F, Cl, Br, and I) complexes. I. Electronic spectra and dissociation pathways

Photodissociation spectra of Mg+-XCH3 (X=F, Cl, Br, and I) complexes have been measured in the ultraviolet region (225-415 nm). Several fragment ions with and without charge transfer (CT), Mg+, XCH3+, MgX+, MgCH3+, CH3+, and X+, were formed by evaporation (intermolecular bond dissociation) and intracluster reaction (intramolecular bond dissociation) via excited electronic states. Branching ratios of these ions were found to depend both on absorption bands and on halogen atoms. The ground states of the complexes were calculated to have geometries in which the Mg atom lies next to X atom of methyl halide molecules. Positive charges of the complexes are confirmed to be almost localized on Mg. Observed absorption bands were assigned to the transitions of the Mg+2P-2S atomic line perturbed by interactions with methyl halide molecules. Branching ratios of fragment ions can be partly explained by the stability of fragment ions and neutral counterparts. From the excited state potential energy curves along the Mg-X bond distance, dissociation reaction after CT was concluded to proceed predissociatively; potential curve crossings between the initially excited states and repulsive CT states may have a crucial role in the formation of CH3+, XCH3+, and X+. In particular, XCH3+ ions were formed via repulsive CT states having a character of electron excitation from Xnp to Mg+3s.

Elastic and charge transfer processes in H++CO collisions

Proton and hydrogen atom time-of-flight spectra in collision energy range of E(trans) = 9.5-30 eV show that the endoergic charge transfer process in the H+ + CO system is almost an order of magnitude less probable than the elastic scattering [G. Niedner-Schatteburg and J. P. Toennies, Adv. Chem. Phys. LXXXII, 553 (1992)]. Ab initio computations at the multireference configuration interaction level have been performed to obtain the ground- and several low-lying excited electronic state potential energy curves in three different molecular orientations namely, H+ approaching the O-end and the C-end (collinear), and H+ approaching the CO molecule in perpendicular configuration with fixed CO internuclear distance. Nonadiabatic coupling terms between the ground electronic state (H+ + CO) and the three low-lying excited electronic states (H + CO+) have been computed and the corresponding diabatic potentials have been obtained. A time-dependent wavepacket dynamics study is modeled first involving only the ground and the first excited states and then involving the ground and the three lowest excited states at the collision energy of 9.5 eV. The overall charge transfer probability have been found to be approximately 20%-30% which is in qualitative agreement with the experimental findings.

Simple and Surprisingly Accurate Approach to the Chemical Bond Obtained from Dimensional Scaling

We present a new dimensional scaling transformation of the Schrödinger equation for the two electron bond. This yields, for the first time, a good description of the bond via D scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential curves for the lowest singlet, triplet, and excited states of H2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.

Electronic structure properties of fluorene-phenylene monomer and its derivatives: TD-DFT study

Fluorene-phenylene (FP) based oligomers and polymers and their derivatives are good candidates for organic blue-light emitting diodes. In this work, the intrinsic properties of the ground and excited states of FP monomer and its derivatives are studied. The ground state optimized structures and energies were obtained using the molecular orbital theory at a restricted (closed-shell) Hartree–Fock level (RHF) and the density functional theory (DFT) as approximated by the various hybrid functionals (RB3LYP, RB3P86, RB3PW91, RMPW1PW91). The ground state potential energy curves or surfaces of FP and its derivatives were obtained using RHF. All derivatives are nonplanar in their electronic ground states. The character and energy of the first 20 singlet–singlet electronic transitions have been investigated by applying the time-dependent DFT approximations, TD-B3LYP, TD-B3P86, TD-B3PW91 and TD-MPW1PW91, to the correspondingly optimized ground state geometries. The lowest singlet state was also studied with the configuration interaction (singles) approach (CIS). For each monomer, the S 1←S 0 electronic transition involves primarily the promotion of an electron from the HOMO to the LUMO, and is strongly polarized along the monomer backbone. Excitation energies are red shifted when side chains are attached to the basic FP unit or when the unit is extended longitudinally. Similar shifts are observed in the HOMO–LUMO gaps as obtained from the ground state DFT calculations. CIS results suggest geometry relaxation in the first singlet excited state. Comparisons between the different theoretical methodologies used to study the electronic ground and excited states are made and discussed.

Generation of potential energy curves for the XΣg+1, BΔg+1, and B′Σg+1 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.

Probing Excited Electronic States Using Vibrationally Mediated Photolysis: Application to Hydrogen Iodide

We measure branching ratios and anisotropy parameters for the photolysis of HI(V)2,J)0) f H + I( 2 P°1/2)/ I( 2 P°3/2) over the wavelength range 297-350 nm. HI is prepared in the V) 2, J ) 0 rovibrational level using direct IR absorption, and the H-atom photofragments are probed with resonance enhanced multiphoton ionization coupled with core-extraction time-of-flight mass spectrometry. The new branching ratio measurements disagree with predictions obtained from ab initio calculations and from the results of an empirical analysis based on experimental values of the HI/DI(V)0) absorption cross sections and branching ratios. Thus, we combine our new data with all existing absorption coefficient and branching fraction data for HI/DI in a global analysis that provides a new empirical determination of the final-state potential curves and transition moment functions for the four excited electronic states contributing to the A-band UV absorption continuum of HI. This analysis yields two models for the radial dependence of the excited state potential energy curves and transition dipole moment functions. The existing data cannot differentiate these models, but this work identifies a range of experiments that would do so. More generally, we demonstrate that photodissociation of vibrationally excited molecules is a sensitive probe of the repulsive excited electronic states encountered in bound-free transitions.

High-intensity and ground-state influence on photoassociation line shapes of 88Sr

The photoassociation probabilities of a sample of ultracold strontium atoms at 1 μK, are analyzed under the systematically varied conditions of frequency detuning and laser intensities, and for different dispersion values of the ground state potential curve. At low intensities, different values of dispersion coefficient of the ground state potential can give the same line shape, but at high enough intensity this multiplicity is lifted and the revealed periodic behavior is broken. The intensity of the laser becomes a control knob in the laboratory and it can be used to make better determinations of the ground state potential energy curve.

Electronic structure of the CdKr lowest Rydberg state determined from laser-excitation spectra using supersonic beam and double optical resonance methods

The lowest $E\phantom{\rule{0.3em}{0ex}}^{3}\ensuremath{\sum}^{+}(6\phantom{\rule{0.3em}{0ex}}^{3}S_{1})$ Rydberg state of the CdKr van der Waals complex was investigated using supersonic-expansion beam and the optical-optical double-resonance methods. Well-defined vibrational levels $A\phantom{\rule{0.3em}{0ex}}^{3}0_{{v}^{\ensuremath{''}}=9}^{+}(^{3}\ensuremath{\Pi})$ and $B\phantom{\rule{0.3em}{0ex}}^{3}1_{{v}^{\ensuremath{''}}=1}^{+}(^{3}\ensuremath{\sum}^{+})$ were used as intermediate states being excited from the $X\phantom{\rule{0.3em}{0ex}}^{1}0^{+}(^{1}\ensuremath{\sum}^{+})$ ground state. Two types of bound-bound excitation spectra of the $E\phantom{\rule{0.3em}{0ex}}^{3}\ensuremath{\sum}^{+}\ensuremath{\leftarrow}A\phantom{\rule{0.3em}{0ex}}^{3}0^{+}$ and $E\phantom{\rule{0.3em}{0ex}}^{3}\ensuremath{\sum}^{+}\ensuremath{\leftarrow}B\phantom{\rule{0.3em}{0ex}}^{3}1$ transitions were observed and recorded. The analyses of the spectra suggest an existence of two, well-defined minima in the $E\phantom{\rule{0.3em}{0ex}}^{3}\ensuremath{\sum}^{+}$-state potential-energy (PE) curve: an inner PE well ${E}_{1}$ with ${D}_{\mathrm{e}}^{\ensuremath{'}}({E}_{1})=1656\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ and an outer well ${E}_{2}$ with ${D}_{\mathrm{e}}^{\ensuremath{'}}({E}_{2})=27\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$, separated from each other by a positive-energy barrier. Combination of bound-bound spectra excited from different intermediate states enabled probing of the $E\phantom{\rule{0.3em}{0ex}}^{3}\ensuremath{\sum}^{+}$-state potential in a relatively large range of internuclear separations $R$ and hence it led to a complete determination of spectroscopical parameters of the $E\phantom{\rule{0.3em}{0ex}}^{3}\ensuremath{\sum}^{+}$-state PE curve. The height of the barrier and its approximate location were also determined. The experimental results of this investigation coincide well with the results of ab initio calculation of Czuchaj and co-workers [Chem. Phys. 248, 1 (1999); Theor. Chem. Acc. 105, 219 (2001)].

Valence-State Atoms in Molecules. 7. Influence of Polarization and Bond-Charge on Spectroscopic Constants of Diatomic Molecules

The polarizable valence-state-atoms-in-molecules (pVSAM) model describes the electron-pair bond in A−B molecules by superposing core-polarized A+B-, A-B+, and A:B structures, whose weights are determined by electronegativity equalization. The polarizable valence state potential energy curve (pVS-PEC) is derived through the systematic improvement of the valence state potential energy curve (VS-PEC) [Gardner, D. O. N.; von Szentpaly, L. J. Phys. Chem. A 1999, 103, 9313] and is given as U(R) = −[(K1/R) + (K2/R4) + (K3/R7)] + (T/R) exp(−λR). The first bracketed term contains the Coulomb, charge-induced dipole, and induced dipole−induced dipole terms, derived from weighted ionic and covalent bond-charge contributions. The potential is tested on a broad variety of homonuclear diatoms and heteronuclear halides and hydrides (a total of 52 molecules). The accuracies of the dimensionless vibration−rotation coupling constant (F) and the anharmonicity constant (G) for the halides of the alkali and coinage metals are ...

The Kramers’ restricted complete active space self-consistent-field method for two-component molecular spinors and relativistic effective core potentials including spin–orbit interactions

The Kramers’ restricted complete active space self-consistent-field (KR-CASSCF) method based upon two-component molecular spinors and relativistic effective core potentials including spin–orbit interactions is implemented, employing the two-step approach, in which the expansion coefficients of configurations and molecular spinors are determined alternately. The present approach allows the influence of spin–orbit interactions to be taken into account in the optimization of one-electron wave function space. Test calculations were performed for the Hg atom, Au− anion, and Tl+ cation with the closed-shell electronic configuration, the ground state potential energy curves of homo-nuclear diatomic molecules, As2, Sb2, and Bi2, over a wide range of inter-nuclear distances, and the bond fission of a polyatomic molecule CH3I. The results show that the KR-CASSCF method properly describes the dissociation of molecules for the fine-structure states. It is also evident that molecular properties are affected by optimized spinors for systems containing heavy atoms such as Bi2 and CH3I at the CASSCF level of theory.

Ground state potential energy curves for He–Kr, Ne–Kr, Ar–Kr, and Kr2: Coupled-cluster calculations and comparison with experiment

Ab initio calculations were performed with the coupled-cluster single and double excitations with perturbative triples correction method using the augmented correlation consistent polarized triple, quadruple, and quintuple zeta basis sets [aug-cc-pVnZ (n=T,Q,5)] for four complexes: He–Kr, Ne–Kr, Ar–Kr, Kr2. For each complex and each basis set a fitted potential energy curve is given. The most accurate results were obtained with the aug-cc-pV5Z basis set supplemented with an additional (3s3p2d2 f1g) set of bond functions. Ab initio potentials were compared to experimental data and the best empirical potentials available. The agreement was good although calculated potentials were found to be too shallow. To better reproduce spectroscopic data, ab initio potentials were modified using a nonlinear least-squares procedure. The modified potentials were developed for He–Kr, Ne–Kr, Ar–Kr, and Kr2, as well as Ne–Ar and Ar2. They all compare favorably with the best available empirical potentials.

Electronic Spectroscopy of the AlSb Molecule: A Theoretical Study

Relativistic configuration interaction calculations are carried out to study the electronic spectrum of the AlSb molecule. Potential energy curves of 44 electronic states within 6 eV of energy are constructed. Spectroscopic constants (re, ωe, Te, De, μe) of the low-lying Λ-S states are computed. The equilibrium bond length and vibrational frequency of the ground state (X3Σ-) of AlSb are estimated to be 2.79 Å and 249 cm-1, respectively. Effects of the spin−orbit coupling on the spectroscopic properties and potential energy curves of states that correlate with the lowest two dissociation limits are investigated. The computed dissociation energy of the ground-state spin component (X3 ) is 1.44 eV. Transition moments of several electric dipole-allowed and spin-forbidden transitions are computed from CI wave functions. Radiative lifetimes of the low-lying excited states of AlSb at the lowest three vibrational levels (v‘ = 0, 1, 2) are estimated. Transitions from the 33Π0+ component to all lower states with ΔΩ = 0, ±1 are predicted. At v‘ = 0, the 33Π0+ component has a lifetime of about 1.26 μs. The electronic states of AlSb are also compared with those of isovalent AlP, GaAs, GaSb, and InSb molecules.

The Fermi model as a key for understanding excited state potential energy curves

The interaction of a Rydberg electron with a ground-state atom is modelled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to the cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for 1Σ + and 3Σ + states of NaH and He 2, for up to the ninth state of a specified symmetry in the former. Overall, good qualitative and in some cases, quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several atomic states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single non-zero potential emerges from the remaining flat manifold. Such behaviour explains, for example, the presence of high barriers at large distances seen in ab initio calculations for the 1,3Σ + 4f states of NaH. For NaH, the Fermi results are generally better for the weaker triplet interactions than the singlets. In case of near-degenerate levels, the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

Calculation of ground and excited state potential energy curves of the MgAr complex using the coupled cluster approximate triples model CC3

Potential curves of the ground and six excited states of MgAr are analysed using the coupled cluster approximate triples approach CC3. The ground state curve is obtained from conventional closed shell energy calculations, and excitation energies to the electronically excited states are obtained solving the CC3 response eigenvalue equation, yielding the potential curves for the excited states. The computed spectroscopic parameters ( R e, ω e, D 0 and T 0) are in good agreement with experimental data when sufficiently large basis sets are used and the counterpoise correction is applied.

The Cs2 ground electronic state by Fourier transform spectroscopy: Dispersion coefficients

This study presents the derivation of an accurate potential energy curve for the ground electronic state of the Cs2 molecule. High resolution laser induced emission spectra data involving vibrational levels of the ground X 1Σg+ state up to v″=135 (16 900 wave numbers) have been determined. The ground state potential energy curve is constructed by combining the inverted perturbation approach for internuclear distances up to 11 Å, with an analytical expression for longer internuclear distances. This potential curve allows an improved derivation of the dissociation energy and of the Coulombic parameters governing the Cs(6s)+Cs(6s) interaction in the electronic ground state, compared with values derived either by calculations or by recent photoassociative spectroscopy measurements. The main constants are C6=6836 (±100) a.u.=32.945 (±0.49)×106 cm−1 Å6, and De=3649.88 (±0.45) cm−1.

Photoinduced dissociation of methylnitrite on Ag( [formula omitted

Electronic excitations and photoinduced electron attachment states of methylnitrite (CH 3ONO) adsorbed on Ag(1 1 1) are investigated by ab initio methods. The calculated ground state energies of the cis and trans isomers of the methylnitrite molecule are nearly degenerate, with the trans structure lower than the cis by 0.03 eV at the CI level. Experimentally, the cis isomer is estimated to be more stable by 0.03 eV. The energy of methylnitrite in its ground electronic state on the silver surface is nearly the same for both isomer configurations and changes only slightly with isomer orientation and adsorption site. In both cis and trans forms, structures in which the internal oxygen points towards the surface and the O(internal)N internuclear axis lies between 30° and 45° from the surface are favored. The calculated adsorption energy is 0.60 eV for the cis isomer. Ground and excited state potential energy curves for dissociation to CH 3O/Ag and NO (gas phase) are calculated at the CI level for both internal electronic excitations and for electron attachment excited states. The calculated ground state dissociation energy is 1.5 eV, a value 0.20 eV less than calculated for the gas phase dissociation. The metal-mediated excitation (electron attachment to the adsorbate and hole in the metal) leads to a repulsive triplet state with a vertical excitation energy of 4.7 eV and negligible singlet–triplet splitting. A second excited state produced by electron excitation within methylnitrite produces distinct singlet and triplet states. The vertical excitation occurs at 2.4 eV for the triplet state and at 3.4 eV for the singlet state. In comparing the methylnitrite/Ag(1 1 1) potential energy surface to that of gas phase methylnitrite, a shallow minimum in the first excited singlet state for the molecule appears only as a plateau in the adsorbate/metal system when the excitation is from within methylnitrite. There is a 10-fold increase in methylnitrite/silver mixing in the metal-mediated excitation as compared to the internal excitation, which may explain the surprising experimental result that dissociation does not follow metal-mediated excitation.