Avoided Curve Crossings Research Articles

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition.

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH3OCH2Cl polarized by a solvent molecule, the ground- and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory.

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications.

We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins.

Assessment of quantum chemical methods and basis sets for excitation energy transfer

The validity of several standard quantum chemical approaches and other models for the prediction of exciton energy transfer is investigated using the HOMO–LUMO excited states of benzene dimer as an example. The configuration interaction singles (CIS), time-dependent Hartree-Fock (TD-HF), time dependent density functional theroy (TD-DFT), and complete-active-space self-consistent-field (CASSCF) methods are applied with a supermolecule approach and compared to the previously established monomer transition density method and the ideal dipole approximation. Strong and physically incorrect admixture of charge-transfer states makes TD-DFT inappropriate for investigations of potential energy surfaces in such dimer systems. CIS, TD-HF and CASSCF perform qualitatively correct. TD-HF seems to be a particularly appropriate method due to its general applicability and overall good performance for the excited state and for transition properties. Double-zeta basis sets with polarisation functions are found to be sufficient to predict transfer rates of dipole allowed excitations. Efficient excitation energy transfer is predicted between degenerate excited states while avoided curve crossings of nearly spaced π-aggregates are identified as a possible trapping mechanism.

Cold Cs Rydberg-gas interactions

We present calculations of potential curves for very high-$n$ $(89D)$ Cs Rydberg-atom pairs, including a background electric field. From these potentials, we show that energy transfer occurs at rates of $\ensuremath{\sim}30--70\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, background electric fields play an important role and dipole-dipole- and quadrupole-quadrupole-induced avoided curve crossings should lead to conversion of electronic to kinetic energy, $n$-changing collisions, and observable ultracold long-range Rydberg molecules.

Avoided curve crossings for the dissociation reaction of the Rydberg H 3O radical into (OH+H 2)

Potential energy curves of the ground and excited states for the dissociation of the Rydberg H 3O radical into (OH+H 2) have been calculated using ab initio Hartree–Fock (HF) and singly and doubly excited configuration interaction (SDCI) methods with a large basis set including Rydberg basis functions. Under C 2v symmetry constraint, the ground 2 A 1 potential curve of (H 3O +)(e −) 3s adiabatically correlates to [ OH( A 2Σ +)+ H 2( X 1Σ g +) ], while the first excited 2 E state of (H 3O +)(e −) 3s correlates to [ OH( X 2Π)+ H 2( X 1Σ g +) ]. The avoided curve crossings between the attractive diabatic states emerging from the cation–anion pair of [OH ++H 2 −] and the repulsive diabatic states from antibonding orbitals of [ OH ∗+ H 2 ] occurs around R OH≃1.8 Å.

Potential energy curves for the dissociation of the Rydberg NH4 radical into (NH2+H2)

Potential energy curves of the ground and excited states for the dissociation of the Rydberg NH4 radical into (NH2+H2) have been calculated using ab initio Hartree–Fock and singly and doubly excited configuration interaction methods with a large basis set including Rydberg basis functions. The ground potential curve (2A1) of the (NH4+)(e−)3s radical adiabatically correlates to the [NH2*(Ã 2A1)+H2(X̃ 1Σg+)] asymptote, while the first excited state (2T2) of (NH4+)(e−)3p correlates to [NH2(X̃ 2B1)+H2(X̃ 1Σg+)]. Two diabatic valence curves emerging from the [NH2*(Ã 2A1)+H2(X̃ 1Σg+)] and [NH2(X̃ 2B1)+H2(X̃ 1Σg+)] asymptotes are repulsively represented, while two diabatic curves from [NH2+(Ã 1A1)+H2−(X̃ 2Σu+)] and [NH2+(X̃ 3B1)+H2−(X̃2 Σu+)] are attractively represented. At shorter than R(NH)≃2.0 Å, the avoided curve crossings between the dissociative diabatic states of the [(NH4+)(e−)Rydberg] radical and the repulsive diabatic states emerging from the antibonding interactions of the [NH2+H2(X̃ 1Σg+)] asymptote are found mainly. While, at larger than R(NH)≃2.0 Å, the avoided curve crossings between the repulsive diabatic states emerging from H2 and the Rydberg states of NH2 and the attractive diabatic states from [NH2+(Ã 1A1)+H2−(X̃ 2Σu+)] and [NH2+(X̃ 3B1)+H2−(X̃ 2Σu+)] are found.

Nonadiabatic dynamics for processes involving multiple avoided curve crossings: Double proton transfer and proton-coupled electron transfer reactions

The extension of the surface hopping method “molecular dynamics with quantum transitions” (MDQT) to double proton transfer and proton-coupled electron transfer reactions is tested by comparison to fully quantum dynamical calculations for simple model systems. These model systems each include four potential energy surfaces and three or four avoided curve crossings. The agreement between the MDQT and fully quantum dynamical calculations provides validation for the application of MDQT to these biologically important processes.

On the bonding in doubly charged diatomics

The potential energy of interacting atomic ions A++B+ often shows a shallow local minimum separated by a broad potential barrier from the dissociation products at much lower energy. Early interpretations of dication potential shapes were based on the similarity of the electronic structure between isoelectronic neutral and ionic species and led to a picture of a chemical bond superimposed on a repulsive Coulomb potential. More recently, barriers in dication potentials have commonly been interpreted as avoided curve crossings involving covalent and ionic structures. In this paper, we demonstrate that the former model is the appropriate one except in cases with very small asymptotic ionic/covalent energy splittings. By deriving dication wavefunctions from their neutral isoelectronic counterparts, we obtain upper bound dication potential curves which show all the characteristic features. By further modeling induction effects, we arrive at an almost quantitative fit of accurateab initio dication potentials. The “chemical bond plus electrostatic repulsion’ interpretation of dication interactions also explains why the accurate calculation of potential curves appears to be much more demanding for dications than for isoelectronic neutrals.

Photoelectron spectroscopy and electronic structure of heavy group IV–VI diatomics

Vibrationally resolved HeI (584 Å) photoelectron spectra of the heavy group IV–VI diatomics SnSe, SnTe, PbSe, and PbTe were obtained with a new high temperature molecular beam source. Ionization potentials and spectroscopic constants are reported for all the ionic states observed. Relativistic complete active space multiconfiguration self-consistent field (MCSCF) followed by multireference singles+doubles relativistic configuration interaction (CI) calculations which included up to 200 000 configurations were made on both the neutral diatomics and their positive ions. Ionization potentials and spectroscopic constants were calculated and were in good agreement with the experimentally measured values. Relativistic CI potential energy curves were calculated for all the neutral ground states and the ionic states involved. Relativistic effects were shown to play an important role in these heavy diatomics. The 2Σ+1/2 and 2Π1/2 states for all four molecular ions showed avoided curve crossings, which resulted in pronounced shoulders in the Ω=1/2 potential energy curves of PbTe+. Experimentally, autoionization transitions were also observed for the PbTe+ spectrum. The importance of the relativistic effect and chemical bonding in the heavy diatomics are discussed.

Dissociation of high np singlet Rydberg levels of H2 by a pulsed electric field.

We have studied the effects of a pulsed electric field on the decay dynamics of high np, J=1 (ng30) singlet Rydberg levels of ${\mathrm{H}}_{2}$ We have discovered that pulsed fields of magnitudes much less than the classical value required for ionization induce a significant degree of dissociative character into levels which normally do not dissociate. This induced dissociation appears to occur during the slew of the field pulse and can be explained in terms of adiabatic passage through avoided curve crossings between the stable J=1 levels and the J=0 and 2 levels which predissociate.

Gerade Rydberg states and n s 3Σ+u(1u,0−u) photoionization spectra of the rare gas dimers (n=2–6)

Transient absorption spectra of rare gas dimer Rydberg transitions in the ultraviolet, visible, and near infrared (220≤λ≤900 nm) spectral regions have been observed in electron beam excited rare gases. The most prominent molecular bands for He2, Ne2, Ar2, Kr2, and Xe2 are assigned to the mp 3Πg←ns 3Σ+u (He:n=2, 3≤m≤10; Ne:n=3, 4≤m≤10; Ar:n=4, 5≤m≤15; Kr:n=5, 6≤m≤16; Xe:n=6, 8≤m≤11) Rydberg series of the dimer. Adiabatic ionization potentials, relative to the ns 3Σ+u state, are determined by extrapolation of the series to their limits (m→∞) to be 34 361.4±30 cm−1 (4.260±0.004 eV) for He2, 34 396.3±25 cm−1 (4.265±0.003 eV) for Ne2, 29 351.9±15 cm−1 (3.639±0.002 eV) for Ar2, 28 428.5±10 cm−1 (3.525±0.001 eV) for Kr2, and 26 664.5±250 cm−1 (3.306±0.031 eV) for Xe2. Absorption bands which are ascribed to m′p 3Σ+g←ns 3Σ+u Rydberg series of Ne2(m′=4,6,8), Ar2(5≤m′≤10), Kr2(6≤m′≤10), and Xe2(m′=8,9) are also reported, and the ns 3Σ+u ionization potentials found to be identical to the respective values quoted above. All of the observed molecular Rydberg states have an A 2Σ+1/2u ion core. The lowest vibrational quanta (ΔG1/2) for the ns 3Σ+u states are determined from vibronic structure in the Rydberg transitions to be 1723 cm−1 for He2, 539 cm−1 for Ne2, 302 cm−1 for Ar2, 172 cm−1 for Kr2, and 135 cm−1 for Xe2, and are consistent with previously reported values. The instability of the ns 3Σ+u metastable state with respect to the dimer ion core potential [D0(A 2Σ+1/2u)−D0(ns 3Σ+u)] is calculated to be 0.508±0.004 eV for He2, 0.681±0.003 eV for Ne2, 0.572±0.002 eV for Ar2, 0.560±0.001 eV for Kr2, and 0.52±0.03 eV for Xe2. Using these values and those reported in the literature for the dissociation energy of the dimer ion A 2Σ+1/2u state, D0(ns 3Σ+u) is estimated (Ne2: 0.67±0.07 eV; Ar2: 0.76±0.02 eV; Kr2: 0.62±0.02 eV; Xe2: 0.52±0.03 eV). By comparing energy level spacings, quantum defects, and absorption oscillator strengths for transitions between molecular or atomic states, the mp 3Πg Rydberg levels appear to correlate with the mp[3/2]2+1S0 atomic asymptotes. An important aspect of the experimental approach is that the diatomic excited states are studied in the vicinity of Re rather than at the van der Waals (ground state) minimum. Chemical forces (as opposed to ion-induced dipole interactions) dominate at small R and the resulting spectra are largely free of congestion arising from the perturbations and avoided curve crossings that are prevalent at large R. Therefore, insight can be obtained into the structure and behavior of molecular Rydberg states in the region near the first ionization limit A 2Σ+1/2u[1(1/2)u].

Valence excited states of CH. I. Potential curves

Ab initio CI calculations have been performed over a wide range of internuclear distances (1.00–20.00 bohr) to obtain the potential curves for the first five valence excited states of CH; X2Π, a4Σ−1, A2Δ, B2Σ−, and C2Σ+. Results, with known experimental values in parentheses, are Re(X2Π) = 2.113 (2.116) bohr, Re(a4Σ−) = 2.053 bohr, Re(A2Δ) = 2.083(2.083) bohr, Re(B2Σ−) = 2.216(2.20) bohr, Re(C2Σ+) = 2.100(2.105) bohr; De(X2Π) = 3.51(3.63) eV, De(a4Σ−) = 2.84 eV, De(A2Δ) = 1.90(2.01) eV, De(B2Σ−) = 0.23(0.40) eV, and De(C2Σ+) = 0.78(0.94) eV. Potential maxima of heights 1284 and 3228 cm−1 are calculated for the B2Σ− and C2Σ+ states, respectively. These maxima are attributed to avoided curve crossings. The a4Σ− state, not observed experimentally, is estimated to lie between 0.62 and 0.76 eV above the X2Π state.