Double Minimum Potential Research Articles

Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction.

We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the time-dependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single- and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.

High-resolution infrared spectroscopy of jet cooled cyclobutyl in the α-CH stretch region: large-amplitude puckering dynamics in a 4-membered ring radical.

Gas-phase cyclobutyl radical (c-C4H7) is generated at a rotational temperature of Trot = 26(1) K in a slit-jet discharge mixture of 70% Ne/30% He and 0.5-0.6% cyclobromobutane (c-C4H7Br). A fully rovibrationally resolved absorption spectrum of the α-CH stretch fundamental band between 3062.9 cm-1 to 3075.7 cm-1 is obtained and analyzed, yielding first precision structural and dynamical information for this novel radical species. The α-CH stretch band origin is determined to be 3068.7887(4) cm-1, which implies only a modest (≈0.8 cm-1) blue shift from rotationally unresolved infrared spectroscopic studies of cyclobutyl radicals in liquid He droplets [A. R. Brown, P. R. Franke and G. E. Douberly, J. Phys. Chem. A, 2017, 121, 7576-7587]. Of particular dynamical interest, a one-dimensional potential energy surface with respect to the ring puckering coordinate is computed at CCSD(T)/ANO2 level of theory and reveals a double minimum Cs puckered geometry, separated by an exceedingly shallow planar C2v transition state barrier (Ebarr ≈ 1 cm-1). Numerical solutions on this double minimum potential yield a zero-point energy for the ground state (Ezero-point ≈ 27 cm-1) greatly in excess of the interconversion barrier. This is indicative of highly delocalized, large amplitude motion of the four-membered ring structure, for which proper vibrationally averaging of the moment of inertia tensor reproduces the experimentally determined inertial defect remarkably well. Finally, intensity alternation in the experimental spectrum due to nuclear spin statistics upon exchange of three indistinguishable H atom pairs (IH = ½) matches Ka + Kc = even : odd = 36 : 28 predictions, implying that the unpaired electron in the radical center lies in an out-of-plane pπ orbital. Thus, high-resolution infrared spectroscopy provides first experimental confirmation of a shallow double minimum ring puckering potential with a highly delocalized ground state wave function peaked at a planar C2v transition state geometry consistent with a cyclobutyl π radical.

Large amplitude inversion tunneling motion in ammonia, methylamine, hydrazine, and secondary amines: From structure determination to coordination chemistry

• Molecular structures of ammonia derivatives captured by spectroscopy. • Tunneling motion as essential information to understand coordination complexes. • Structures and internal dynamics from experimental and theoretical points of view. • Using the structures of isolated ligand to determine the structure of complexes. Inversion tunneling in a symmetric double minimum potential is a challenging large amplitude motion problem which causes all rotational energy levels to split into a symmetric and an antisymmetric level. Not like other types of large amplitude motion such as internal rotation, inversion tunneling appears much rarer, but the fundamental knowledge gained from this motion is essential to understand the complex structures in coordination chemistry. A double minimum potential needed for inversion tunneling requires the symmetry of the frame to which the inversion object is attached to be C s or higher, while there is no restriction on the symmetry of the frame for internal rotation. This review summarizes four most classic examples of molecules featuring inversion tunneling motion and their coordination complexes. The textbook example, ammonia, with its umbrella motion during which the nitrogen atom passes from one side of the plane formed by the three hydrogens to the other, will be presented with information on its group theoretical considerations, theoretical studies, electronic ground state spectra in the infrared range, and its coordination complexes, especially those formed with calcium and copper. In the second classic example, methylamine, CH 3 NH 2 , the inversion motion of the amino group –NH 2 is coupled with a methyl internal rotation –CH 3 . The spectrum of methylamine can be treated using a tunneling formalism applying the G 12 permutation-inversion symmetry group. Extensive studies on the ground state, the first and second excited torsional states ν 15 , the inversion wagging state ν 9 , and the C-N stretching band ν 8 exist along with their combinations. Pertubations and blends have made the analysis of methylamine very challenging. The third subject is on hydrazine with complex internal dynamics governed by three large amplitude motions: two –NH 2 tunneling motions and an internal rotation (torsion) of the two amino groups around the N-N bond. Regarding the spectrum of hydrazine, the vibrational ground state lies in the microwave region. The first, second, and third excited torsional band ν 7 , symmetric wagging ν 6 , and asymmetric wagging ν 12 are found in the infrared range. Group theoretical treatment and tunneling formalism can only be used to fit sub-bands individually, while global fits still remain a difficult task. Metal complexes with hydrazine and methylamine are introduced, proving the importance of spectroscopic understanding of molecular structures for the knowledge of coordination chemistry. Finally, secondary amines feature inversion tunneling of the hydrogen atom attached to the nitrogen, which is accompanied by two methyl internal rotations but not coupled with them so that they can be treated separately. For this class of molecules, only spectra of the vibrational ground state in the microwave domain will be considered.

Phonon-assisted proton tunneling in the hydrogen-bonded dimeric selenates of Cs3H(SeO4)2.

In phases III and IV of Cs3H(SeO4)2, the vibrational state and intrabond transfer of the proton in the dimeric selenates are systematically studied with a wide range of absorbance spectra, a spin-lattice relaxation rate of 1H-NMR (T1 -1), and DFT calculations. The OH stretching vibrations have extremely broad absorption at around 2350 (B band) and 3050 cm-1 (A band), which originate from the 0-1 and 0-2 transitions in the asymmetric double minimum potential, respectively. The anharmonic-coupling calculation makes clear that the A band couples not only to the libration but also to the OH bending band. The vibrational state (nano-second order) is observed as the response of the proton basically localized in either of the two equivalent sites. The intrabond transfer between those sites (pico-second order) yields the protonic fluctuation reflected in T1 -1. Together with the anomalous absorption [νp2 phonon, libration, tetrahedral deformation (δ440), and 610-cm-1 band], we have demonstrated that the intrabond transfer above 70 K is dominated by the thermal hopping that is collectively excited at 610 cm-1 and the phonon-assisted proton tunneling (PAPT) relevant to the tetrahedral deformation [PAPT(def)]. Below 70 K, T1 -1 is largely enhanced toward the antiferroelectric ordering and the distinct splitting emerges in the libration, which dynamically modulates the O(2)-O'(2) distance of the dimer. The PAPT(lib) associated with the libration is confirmed to be a driving force of the AF ordering.

Quenched tunneling in ammonia

Quantum Mechanics Inversion between two energetically equivalent umbrella-spaced configurations in ammonia (NH3) is a classic textbook example of tunneling in a symmetric double-minimum potential. Park et al. report on how a very strong direct-current electric field, as powerful as intermolecular interactions, can suppress this quantum mechanical phenomenon in the system. They observed that NH3 molecules isolated in a solid argon matrix at 10 kelvin strongly orient along the external field direction and that, as the field is increased up to 200 million volts per meter, their energy states shift, eventually quenching the tunneling from the normal state to the inverted one. The observed changes are reversible and open up opportunities for manipulating tunneling dynamics in many other molecules. Proc. Natl. Acad. Sci. U.S.A. 116 , 23444 (2019).

Millimeter-wave spectroscopy of HDC=CH.

Rotational transitions of the mono(β)-deuterated vinyl radical, HDC=CH, produced in a supersonic jet expansion by the ArF excimer laser photolysis, were observed by millimeter-wave spectroscopy. The b-type rotational transitions together with the weak a-type transitions were observed only for the lower component of the tunneling doublet, and no tunneling-rotation transitions connecting the lower and upper components were observed, suggesting that state mixing between the two components is negligibly small. The derived molecular constants such as the A rotational constant, Fermi contact interaction constants, and magnetic dipolar interaction constants indicate that the carrier of the observed spectrum is the trans-form of HDC=CH isomers, where the α-proton is located on the opposite side of the β-deuteron. The present conclusion of the trans-form of HDC=CH was also supported by the ab initio calculation in the CCSD(T)/cc-pVTZ level since the trans-form is calculated to be located by 30.04 cm-1 lower than the cis-form due to the difference in the zero point energy. As a result, the tunneling components in the ground state of HDC=CH behave as two different isomers localized at the trans- and cis-wells of the asymmetric double minimum potential. Observed hyperfine constants for HDC=CH were compared with those for H2C=CH to be consistent with each other.

The frequency-domain infrared spectrum of ammonia encodes changes in molecular dynamics caused by a DC electric field

Ammonia is special. It is nonplanar, yet in v = 1 of the umbrella mode (ν2) its inversion motion is faster than J = 0↔1 rotation. Does the simplicity of the Chemist's concept of an electric dipole moment survive the competition between rotation, inversion, and a strong external electric field? NH3 is a favorite pedagogical example of tunneling in a symmetric double-minimum potential. Tunneling is a dynamical concept, yet the quantitative characteristics of tunneling are expressed in a static, eigenstate-resolved spectrum. The inverting-umbrella tunneling motion in ammonia is both large amplitude and profoundly affected by an external electric field. We report how a uniquely strong (up to 108 V/m) direct current (DC) electric field causes a richly detailed sequence of reversible changes in the frequency-domain infrared spectrum (the v = 0→1 transition in the ν2 umbrella mode) of ammonia, freely rotating in a 10 K Ar matrix. Although the spectrum is static, encoded in it is the complete inter- and intramolecular picture of tunneling dynamics.

Hydrated Excess Protons in Acetonitrile/Water Mixtures: Solvation Species and Ultrafast Proton Motions

The solvation structure of protons in aqueous media is highly relevant to electric properties and to proton transport in liquids and membranes. At ambient temperature, polar liquids display structural fluctuations on femto- to picosecond time scales with a direct impact on proton solvation. We use two-dimensional infrared (2D-IR) spectroscopy to follow proton dynamics in acetonitrile/water mixtures with the Zundel cation H5O2+ prepared in neat acetonitrile as a benchmark. The 2D-IR spectra of the proton transfer mode of H5O2+ demonstrate stochastic large-amplitude motions in the double-minimum proton potential, driven by fluctuating electric fields. In all cases, the excess proton is embedded in a water dimer, forming an H5O2+ complex as the major solvation species. This observation is rationalized by quantum mechanics/molecular mechanics molecular dynamics simulations including up to four water molecules embedded in acetonitrile. The Zundel motif interacts with its closest water neighbor in an H7O3+ unit without persistent proton localization.

Supersonic jet spectroscopy of parent hemiporphycene: Structural assignment and vibrational analysis for S0 and S1 electronic states.

Hemiporphycene (HPc), a constitutional isomer of porphyrin, is studied under supersonic expansion conditions by means of laser-induced fluorescence, visible-visible hole-burning experiments, single vibronic level fluorescence techniques, and quantum chemical calculations. Only one trans form of jet-cooled HPc is observed, in contrast to solution studies that evidence a mixture of two trans tautomeric forms separated in energy by ∼1 kcal/mol. Reliable structural assignment is provided by simulating absorption and emission patterns at the density functional theory and time-dependent density functional theory levels of theory. The vibronic spectra are nicely reproduced for both electronic ground and lowest excited singlet states for the most stable trans form. In contrast to another porphyrin isomer, porphycene (Pc), no tunneling or photo-induced hydrogen transfer is detected. The lower symmetry of HPc compared with Pc and the concomitant non-equivalent positions of the inner-cavity nitrogen atoms result in a non-symmetric double minimum potential for tautomerization, larger energy barrier, and a longer tunneling distance, with the average intramolecular hydrogen bond length larger in HPc than in Pc. HPc readily forms hydrates that show red-shifted absorption relative to the bare molecule.

Coexistence, mixing and fluctuation of nuclear shapes

The coexistence between near-spherical and well-deformed shapes in nuclear systems is studied by a schematic collective model employing a double-minimum phenomenological potential with an accounted centrifugal contribution from the kinetic energy. The quantum tunneling between the two deformation minima depends on the characteristics of the separating barrier and is gauged by the density probability distribution of deformation in the ground and excited states. Various degrees of overlap between the two states are associated to shape coexistence with and without mixing or to simple shape fluctuation phenomena. The effect of the interaction between deformation configurations on the transition observables is exemplified on the 76Kr nucleus.

Na2 Vibrating in the Double-Well Potential of State 2 1Σu+ (JM = 00): A Pulsating "Quantum Bubble" with Antagonistic Electronic Flux.

The theory of concerted electronic and nuclear flux densities associated with the vibration and dissociation of a multielectron nonrotating homonuclear diatomic molecule (or ion) in an electronic state 2S+1Σg,u+ (JM = 00) is presented. The electronic population density, nuclear probability density, and nuclear flux density are isotropic. A theorem of Barth , presented in this issue, shows that the electronic flux density (EFD) is also isotropic. Hence, the evolving system appears as a pulsating, or exploding, "quantum bubble". Application of the theory to Na2 vibrating in the double-minimum potential of the 2 1Σu+ (JM = 00) excited state reveals that the EFD consists of two antagonistic components. One arises from electrons that flow essentially coherently with the nuclei. The other, which is oppositely directed (i.e., antagonistic) and more intense, is due to the transition in electronic structure from "Rydberg" to "ionic" type as the nuclei traverse the potential barrier between inner and outer potential wells. This "transition" component of the EFD rises and falls sharply as the nuclei cross the barrier.

Polyacetylene: Myth and Reality.

Polyacetylene, the simplest and oldest of potentially conducting polymers, has never been made in a form that permits rigorous determination of its structure. Trans polyacetylene in its fully extended form will have a potential energy surface with two equivalent minima. It has been assumed that this results in bond length alternation. It is, rather, very likely that the zero-point energy is above the Peierls barrier. The experimental studies that purport to show bond alternation are reviewed and shown to be compromised by serious experimental inconsistencies or by the presence, for which there is considerable evidence, of finite chain polyenes. In this view, addition of dopants results in conductivity by facilitation of charge transport between finite polyenes. The double minimum potential that necessarily occurs for polyacetylene, if viewed as the result of elongation of finite chains, originates from admixture of the 11Ag ground electronic state with the 21Ag excited electronic singlet state. This excitation is diradical (two electron) in character. The polyacetylene limit is an equal admixture of these two 1Ag states making theory intractable for long chains. A method is outlined for preparation of high molecular weight polyacetylene with fully extended chains that are prevented from reacting with neighboring chains.

Communication: Electronic flux induced by crossing the transition state.

We present a new effect of chemical reactions, e.g., isomerizations, that occurs when the reactants pass along the transition state, on the way to products. It is based on the well-known fact that at the transition state, the electronic structure of one isomer changes to the other. We discover that this switch of electronic structure causes a strong electronic flux that is well distinguishable from the usual flux of electrons that travel with the nuclei. As a simple but clear example, the effect is demonstrated here for bond length isomerization of Na2 (21Σu+), with adiabatic crossing the barrier between the inner and outer wells of the double minimum potential that support different "Rydberg" and "ionic" type electronic structures, respectively.

The role of water in the anomalies of pyro- and thermodepolarization properties of pyroactive polymer films at stepwise heating

The paper presents the results of investigations of the temperature dependencies of pyroelectric coefficient and thermodepolarization currents of pyroelectric polymer films (hydrophobic VDF/TrFE copolymer and hydrophilic Langmuir films of azo compounds), which were prepared using water. The anomalies of these properties were observed at 4, 28, 35, 45°C for films of azo compounds and 20, 35, 49, 72 and 100°C for VDF/TrFE. These temperature points are close to temperatures of anomalies of physical properties of water. At the listed temperature points, water clusters and the molecule itself are destroyed. Similar anomalies have been previously observed in crystallohydrates, “polymer-water” systems and ferroelectrics of Triglycine Sulphate family, in the structure of which there is a network of OH…O hydrogen bonds of the same length as in water. The key property of the hydrogen bond is the presence of discrete protons energy levels, which at stepwise heating (slow kinetics) leads to the transformation or destruction of the hydrogen-bonding network, as well as to the refilling of proton energy levels in the double minimum potential, the release of deep traps, and to the change of charge carrier types, their mobility and conducting paths.

Molecular chirality: A new approach from a dynamical point of view.

The double minimum potential (DMP), which Hund assumed to explain the quantum-mechanical stability of enantiomers, was discussed, by citing three typical examples of DMP: inversion, internal rotation, and puckering. They expanded the classical scope of chirality, as defined by Kelvin, and indicated that a new bridge could be formed between the three low-frequency DMP modes and the asymmetric syntheses of chiral molecules.

Fluorine atom influence on intramolecular hydrogen bonding, isomerization and methyl group rotation in fluorinated acetylacetones

1-Fluoro-pentane-2,4-dione (monofluoroacetylacetone, MFAA) is an asymmetric β-diketone with a strong intramolecular hydrogen bond similar to acetylacetone (AA) and its fluorinated analogs 1,1,1-trifluoro-(TFAA), and 1,1,1,5,5,5-hexafluoroacetylacetone (HFAA). The presence of a fluorine atom in MFAA has the potential to open an HF elimination channel in its gas-phase photochemistry motivating this study of MFAA hydrogen bonding by computer modeling using Density Functional Theory (DFT). As a context, we also report DFT modeling of AA and selected fluorinated acetylacetones: 1,1-difluoro-pentane-2,4-dione (difluoroacetylacetone, DFAA), TFAA, and HFAA. The most stable molecular structure for all three asymmetric β-diketones (MFAA, DFAA and TFAA) is the isomer with the fluoromethyl group proximal to the carbonyl carbon; in comparison to the proton transfer isomer, which has the fluoromethyl group proximal to the hydroxyl carbon, the carbonyl isomer is lower in energy by 5.1–5.5kJmol−1 (B3LYP/cc-pVTZ) and 2.1–3.7kJmol−1 (MP2/Aug-cc-pVTZ). We also report hydrogen bond strengths, barriers to proton transfer interconversion and barriers to rotation of the methyl/fluoromethyl groups. Our study, the first to report molecular structure information on MFAA and DFAA, indicates that the most stable chelated isomer of MFAA is not the structure with the strongest hydrogen bond as conventionally determined. Our modeling also reveals a coupling between proton transfer isomerization and methyl group rotation, and an unexpected double-minimum potential for the rotation of the fluoromethyl group of MFAA.

Supersonic Jet Spectroscopy and Density Functional Theory Study of Isomeric Diazines: 1,4- and 1,8-Diazatriphenylene. Why Do They Differ So Deeply?

We report on laser-induced fluorescence excitation and dispersed fluorescence spectra of two isomeric compounds: 1,4- and 1,8-diazatriphenylene (1,4- and 1,8-DAT) isolated in supersonic molecular jets, and their 1:1 complexes with protic solvents. We found that the ground and excited state vibronic patterns of bare 1,4-DAT differ significantly from those of 1,8-DAT, and those of the complexes of both isomers. A marked activity of several out-of-plane vibrations in 1,4-DAT and the symptoms of the distortion of the S1 excited molecule were diagnosed from the vibronic spectra, whereas planar structures were predicted for 1,8-DAT in S0 and S1 states. An anharmonic double-minimum potential along an out-of-plane coordinate has been derived and used to predict higher overtones of the S1 state vibration at 113 cm-1. Large enhancement of fluorescence was observed upon formation of 1:1 complexes of 1,4-DAT with water or methanol, which is explained in terms of an increased separation of interacting (n,π*) and (π,π*) electronic states in the H-bonded complexes, and/or a suppression of the intersystem crossing process.

LEVEL: A computer program for solving the radial Schrödinger equation for bound and quasibound levels

This paper describes program LEVEL, which can solve the radial or one-dimensional Schrödinger equation and automatically locate either all of, or a selected number of, the bound and/or quasibound levels of any smooth single- or double-minimum potential, and calculate inertial rotation and centrifugal distortion constants and various expectation values for those levels. It can also calculate Franck–Condon factors and other off-diagonal matrix elements, either between levels of a single potential or between levels of two different potentials. The potential energy function may be defined by any one of a number of analytic functions, or by a set of input potential function values which the code will interpolate over and extrapolate beyond to span the desired range.

Observation of b2 symmetry vibrational levels of the SO2 C̃ (1)B2 state: Vibrational level staggering, Coriolis interactions, and rotation-vibration constants.

The C̃ (1)B2 state of SO2 has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. However, low-lying levels with odd quanta of antisymmetric stretch (b2 vibrational symmetry) have not previously been observed because transitions into these levels from the zero-point level of the X̃ state are vibronically forbidden. We use IR-UV double resonance to observe the b2 vibrational levels of the C̃ state below 1600 cm(-1) of vibrational excitation. This enables a direct characterization of the vibrational level staggering that results from the double-minimum potential. In addition, it allows us to deperturb the strong c-axis Coriolis interactions between levels of a1 and b2 vibrational symmetry and to determine accurately the vibrational dependence of the rotational constants in the distorted C̃ electronic state.

The origin of unequal bond lengths in the C̃ (1)B2 state of SO2: Signatures of high-lying potential energy surface crossings in the low-lying vibrational structure.

The C̃ (1)B2 state of SO2 has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. The asymmetry in the potential energy surface is expressed as a staggering in the energy levels of the ν3(') progression. We have recently made the first observation of low-lying levels with odd quanta of v3('), which allows us-in the current work-to characterize the origins of the level staggering. Our work demonstrates the usefulness of low-lying vibrational level structure, where the character of the wavefunctions can be relatively easily understood, to extract information about dynamically important potential energy surface crossings that occur at much higher energy. The measured staggering pattern is consistent with a vibronic coupling model for the double-minimum, which involves direct coupling to the bound 2 (1)A1 state and indirect coupling with the repulsive 3 (1)A1 state. The degree of staggering in the ν3(') levels increases with quanta of bending excitation, which is consistent with the approach along the C̃ state potential energy surface to a conical intersection with the 2 (1)A1 surface at a bond angle of ∼145°.