Van Der Waals Dimers Research Articles

Through-space scalar spin-spin coupling: from rigid intramolecular cases to short-lived van der Waals complexes.

We will discuss, with the help of few selected examples, how the concept of through-space scalar spin-spin coupling between non covalently bonded nuclei has evolved in recent years. We will first present systems where 'no covalent bond' actually means that the two atoms are separated by a large number of bonds; then we will see cases where it is referred to true van der Waals dimers, but with the two atoms somehow constrained in their positions; we will finish with the most recent examples of liquids and even gaseous mixtures with full translational degrees of freedom in a regime of intermolecular/interatomic fast exchange.

Unusual Dynamics and Vibrational Fingerprints of van der Waals Dimers Formed by Linear Molecules and Rare-Gas Atoms.

Detailed structural, dynamical, and vibrational analyses have been performed for systems composed of linear triatomic molecules solvated by a single rare-gas atom, He, Ne, or Ar. Among the chromophores of these van der Waals (vdW) dimers, there are four neutral molecules (CO2, CS2, N2O, and OCS) and six molecular cations (HHe2+, HNe2+, HAr2+, HHeNe+, HHeAr+, and HNeAr+), both of apolar and polar nature. Following the exploration of bonding preferences, high-level four-dimensional (4D) potential energy surfaces (PESs) have been developed for 24 vdW dimers, keeping the two intramonomer bond lengths fixed. For these 24 complexes, over 1500 bound vibrational states have been obtained via quasi-variational nuclear-motion computations, employing exact kinetic-energy operators together with the accurate 4D PESs and their 2D/3D cuts. The reduced-dimensional (2D to 4D) dimer models have been compared with full-dimensional (6D) ones in the cases of the neutral CO2·Ar and charged HHe2+·He dimers, corroborating the high accuracy of the 2D to 4D vibrational energies. The reduced-dimensional models suggest that (a) while the equilibrium structures are T-shaped and planar, the effective ground-state structures are nonplanar, (b) certain bound states belong to collinear molecular structures, even when they are not minima, (c) the vdW vibrations are heavily mixed and many states have amplitudes corresponding to both the T-shaped and collinear structures, (d) there are a few dimers, for which even some of the vdW fundamentals lie above the first dissociation limit, and (e) the vdW vibrations are almost fully decoupled from the intramonomer bending motion.

Excitonic Coupling in Fluorene-Based Bichromophoric Systems: Vibrational Quenching and the Transition from Weak to Intermediate Coupling.

Excimeric systems (i.e., excited dimers) have well served as model compounds for the study of the delocalization of electronic energy over weakly interacting chromophores. However, there remain relatively few isolated systems in which such interactions can be studied experimentally at a level to afford detailed comparisons with theory. In this Article, we examine a series of covalently and noncovalently linked dimers of fluorene, as a model aromatic chromophore, where the formation of excimers requires a π-stacked, cofacial orientation at van der Waals contact. Building upon a series of seminal prior studies that examined vibronic quenching of the excitation interaction in van der Waals dimers, the key question that we sought to address here is whether a single quenching factor could reproduce experimental excitonic splittings across a series of covalently and noncovalently linked bichromophoric systems built from the same chromophore. In comparing experimentally measured excitonic splittings with calculated static splittings using time-dependent density functional methods, we find that all systems save one fall on a line with a slope of 0.080(8), reflecting a vibrational quenching of roughly 1 order of magnitude. The outlier, which shows a significantly reduced quenching factor, represents a cyclophane-linked system where the fluorene moieties are constrained in a cofacial arrangement. We argue that this system evidences the transition from the weak to intermediate coupling regime.

Theoretical study of infrared spectrum for Ar–AgF complex

In this work, we investigate the infrared spectrum of the Ar–AgF complex by using two methodologies. The first is performed by the computation of full-dimensional dynamics, and the second is obtained by solving the full-dimensional Hamiltonian separately. The vibrational shift, which shows excellent agreement with each other, is determined to be 29.11 cm–1 from the former methodology and 29.14 cm–1 from the latter methodology upon AgF excitation in the Ar–AgF complex. For the latter methodology, the contribution from intermolecular interactions is determined to be a positive value of 39.45 cm–1, while that from intramolecular interactions is only 0.51 cm–1, which is the difference of the intermolecular force acting on the AgF monomer. The contribution from intermolecular-intramolecular coupling interactions is determined to be a negative value of –10.82 cm–1. Since the full-dimensional Hamiltonian of the van der Waals dimer can be divided into three sub-units, the latter methodology is named the 3H-solution model. Based on the potential energy surfaces and bound state calculations, infrared spectra were predicted for the fundamental and the first two combination bands of the Ar–AgF complex.

Spectroscopic Properties of the Alkali-Krypton Diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals Systems Including the Spin-Orbit Coupling.

Using an ab initio approach based on pseudopotential technique, pair potential approach, core polarization potentials, and large Gaussian basis sets, we investigate interaction of heavy alkali-krypton diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals dimers. In this context, the core-core interactions for M+-Kr (M = Rb, Cs, and Fr) are calculated at coupled-cluster single and double excitation (CCSD) level and included in the total potential energy. Therefore, the potential energy curves are performed for 14 electronic states: eight of 2Σ+ symmetry, four of 2Π symmetry, and two of 2Δ symmetry. Furthermore, for each M-Kr dimer, the spin-orbit coupling has been considered for the B2Σ+, A2Π, 32Σ+, 22Π, 52Σ+, 32Π, and 12Δ states. In addition, the transition dipole moment has been determined, including the spin-orbit effect using the rotational matrix issued from the spin-orbit potential energy calculations.

Thermodynamic Properties of van der Waals Dimers and Trimers of Nonpolar Gases and Their Correlation with Lennard-Jones Potential Well Depths.

A method of unifying the equilibrium thermodynamic properties ΔHo and ΔGo relating to the van der Waals dimers and trimers of 15 nonpolar gases (He-Xe, H2, D2, CH4, CF4, ethene, ethane, CO2, SF6, propane, and neopentane) is described. Values of ΔHo and ΔGo, obtained at the reduced temperature Tr = 0.7, show good correlation with the respective Lennard-Jones pair potential well depth, calculated from the monomer critical temperature and the acentric factor. Such relationships present the opportunity to estimate the van der Waals dimer and trimer thermodynamic properties of other nonpolar molecules, and examples of seven such applications are given. It is found that the enthalpies of dimerization and trimerization of the 15 gases are about 21 and 29% of the respective condensation enthalpies, providing information about the thermodynamics of small clusters in relation to liquefaction.

Fast intersystem crossing in the tetracene dimers as a source of “dark” state

Tetracene (Tc) is a prototype material undergoing singlet fission (SF), the formation of a pair of triplet excitons from a singlet exciton. The tetracene dimer Tc2 is supposed to be a structural unit providing SF behavior. This work is devoted to the study of the mechanism of singlet exciton decay in van der Waals dimers of Tc2. A nanosecond pump-probe approach is used, tuning both pumping and probing wavelengths. It is shown that the photoexcitation of both the Tc monomer and dimer gives rise to a triplet Tc(T1) with very similar photoionization spectra, indicating an intersystem crossing (ISC) as the source of Tc(T1) in both cases. This finding, together with the very short lifetime of the singlet exciton in van der Waals Tc2 dimers as reported earlier in the literature, indicates that the ISC process is much faster in the dimer than in bare Tc. The factors that increase the rate of ISC in donor–acceptor complexes are the low-lying charge-transfer state in the Tc2 dimer and the proximity in the energy between the singlet S1 and triplet T2 states in tetracene. This fast ISC process is assigned to the temperature-independent process reported earlier in the literature, leading to a “dark” state in tetracene. The results obtained indicate that the dimer of tetracene can be considered to be a structural unit responsible for both fast ISC and SF processes.

Diffuse Basis Functions for Relativistic s and d Block Gaussian Basis Sets

Diffuse s, p, and d functions have been optimized for use with previously reported relativistic basis sets for the s and d blocks of the periodic table. The functions were optimized on the 4:1 weighted average of the s2 and p2 configurations of the anion, with the d shell in the dn+1 configuration for the d blocks. Exponents were extrapolated for groups 2 and 12, which have unstable or weakly bound anions. The diffuse basis sets have been tested by application to calculations of electron affinities of the group 11 elements (Cu, Ag, and Au), double electron affinities of the group 11 monocations, and potential energy curves of Mg2 and Ca2 van der Waals dimers, as well as some response properties of the group 1 anions (Rb-, Cs-, and Fr-), the group 2 elements (Sr, Ba, and Ra), and RbLi, CsLi, and FrLi molecules.

4-component relativistic Hamiltonian with effective QED potentials for molecular calculations.

We report the implementation of effective quantum electrodynamics (QED) potentials for all-electron four-component relativistic molecular calculations using the DIRAC code. The potentials are also available for two-component calculations, being properly picture-change transformed. The latter point is important; we demonstrate through atomic calculations that picture-change errors are sizable. Specifically, we have implemented the Uehling potential [E. A. Uehling, Phys. Rev. 48, 55 (1935)] for vacuum polarization and two effective potentials [P. Pyykkö and L.-B. Zhao, J. Phys. B: At., Mol. Opt. Phys. 36, 1469 (2003) and V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005)] for electron self-energy. We provide extensive theoretical background for these potentials, hopefully reaching an audience beyond QED specialists. We report the following sample applications: (i) We first confirm the conjecture of P. Pyykkö that QED effects are observable for the AuCN molecule by directly calculating ground-state rotational constants B0 of the three isotopomers studied by microwave spectroscopy; QED brings the corresponding substitution Au-C bond length rs from 0.23 to 0.04pm agreement with experiment. (ii) In regard to spectroscopic constants of van der Waals dimers M2 (M = Hg, Rn, Cn, Og), QED induces bond length expansions on the order of 0.15(0.30) pm for row 6(7) dimers. (iii) We confirm that there is a significant change of valence s population of Pb in the reaction PbH4 → PbH2 + H2, which is thereby a good candidate for observing QED effects in chemical reactions, as proposed in [K. G. Dyall et al., Chem. Phys. Lett. 348, 497 (2001)]. We also find that whereas in PbH4 the valence 6s1/2 population resides in bonding orbitals, it is mainly found in nonbonding orbitals in PbH2. QED contributes 0.32 kcal/mol to the reaction energy, thereby reducing its magnitude by -1.27%. For corresponding hydrides of superheavy flerovium, the electronic structures are quite similar. Interestingly, the QED contribution to the reaction energy is of quite similar magnitude (0.35 kcal/mol), whereas the relative change is significantly smaller (-0.50%). This curious observation can be explained by the faster increase in negative vacuum polarization over positive electron self-energy contributions as a function of nuclear charge.

Time-Resolved Imaging of Stochastic Cascade Reactions over a Submillisecond to Second Time Range at the Angstrom Level

Many chemical reactions, such as multistep catalytic cycles, are cascade reactions in which a series of transient intermediates appear and disappear stochastically over an extended period. The mechanisms of such reactions are challenging to study, even in ultrafast pump-probe experiments. The dimerization of a van der Waals dimer of [60]fullerene producing a short carbon nanotube is a typical cascade reaction and is probably the most frequently studied in carbon materials chemistry. As many as 23 intermediates were predicted by theory, but only the first stable one has been verified experimentally. With the aid of fast electron microscopy, we obtained cinematographic recordings of individual molecules at a maximum frame rate of 1600 frames per second. Using Chambolle total variation algorithm processing and automated cross-correlation image matching analysis, we report on the identification of several metastable intermediates by their shape and size. Although the reaction events occurred stochastically, varying the lifetime of each intermediate accordingly, the average lifetime for each intermediate structure could be obtained from statistical analysis of many cinematographic images for the cascade reaction. Among the shortest-living intermediates, we detected one that lasted less than 3 ms in three independent cascade reactions. We anticipate that the rapid technological development of microscopy and image processing will soon initiate an era of cinematographic studies of chemical reactions and cinematic chemistry.

The influence of a solvent environment on direct non-covalent interactions between two molecules: A symmetry-adapted perturbation theory study of polarization tuning of π–π interactions by water

High-level quantum chemical computations have provided significant insight into the fundamental physical nature of non-covalent interactions. These studies have focused primarily on gas-phase computations of small van der Waals dimers; however, these interactions frequently take place in complex chemical environments, such as proteins, solutions, or solids. To better understand how the chemical environment affects non-covalent interactions, we have undertaken a quantum chemical study of π–π interactions in an aqueous solution, as exemplified by T-shaped benzene dimers surrounded by 28 or 50 explicit water molecules. We report interaction energies (IEs) using second-order Møller–Plesset perturbation theory, and we apply the intramolecular and functional-group partitioning extensions of symmetry-adapted perturbation theory (ISAPT and F-SAPT, respectively) to analyze how the solvent molecules tune the π–π interactions of the solute. For complexes containing neutral monomers, even 50 explicit waters (constituting a first and partial second solvation shell) change total SAPT IEs between the two solute molecules by only tenths of a kcal mol−1, while significant changes of up to 3 kcal mol−1 of the electrostatic component are seen for the cationic pyridinium–benzene dimer. This difference between charged and neutral solutes is attributed to large non-additive three-body interactions within solvated ion-containing complexes. Overall, except for charged solutes, our quantum computations indicate that nearby solvent molecules cause very little “tuning” of the direct solute–solute interactions. This indicates that differences in binding energies between the gas phase and solution phase are primarily indirect effects of the competition between solute–solute and solute–solvent interactions.

The thermodynamics of the van der Waals dimer and trimer formation in gaseous carbon dioxide and methane and their heterodimers with dinitrogen

The equilibrium thermochemical properties of the dimers and trimers of the greenhouse gases carbon dioxide and methane, as well as their heterodimers with dinitrogen, have been calculated from the CO2 and CH4 equations of state (EOSs) and statistical mechanics. The standard dimer and trimer equilibrium constants, along with the respective ΔHoandΔSo values are reported for CO2 and CH4 between 220 and 260, and 95 and 135 K, respectively, and for the heterodimers between 100 and 250 K. Statistical mechanical calculations based on experimental and computational data of the dimers provide qualitative agreement with the EOS results. The equilibrium thermochemical properties of the CH4 dimer and the CO2–N2 and CH4–N2 heterodimers are calculated using a Morse potential to represent pairwise interactions in an “atom–diatom” model that accounts for both bound and metastable rovibrational states.

Ionization and electron excitation of C60 in a carbon nanotube: A variable temperature/voltage transmission electron microscopic study

There is increasing attention to chemical applications of transmission electron microscopy, which is often plagued by radiation damage. The damage in organic matter predominantly occurs via radiolysis. Although radiolysis is highly important, previous studies on radiolysis have largely been descriptive and qualitative, lacking in such fundamental information as the product structure, the influence of the energy of the electrons, and the reaction kinetics. We need a chemically well-defined system to obtain such data and have chosen as a model a variable-temperature and variable-voltage (VT/VV) study of the [2 + 2] dimerization of a van der Waals dimer [60]fullerene (C60) to C120 in a carbon nanotube (CNT), as studied for several hundred individual reaction events at atomic resolution. We report here the identification of five reaction pathways that serve as mechanistic models of radiolysis damage. Two of them occur via a radical cation of the specimen generated by specimen ionization, and three involve singlet or triplet excited states of the specimen, as initiated by electron excitation of the CNT, followed by energy transfer to the specimen. The [2 + 2] product was identified by measuring the distance between the two C60 moieties, and the mechanisms were distinguished by the pre-exponential factor and the Arrhenius activation energy—the standard protocol of chemical kinetic studies. The results illustrate the importance of VT/VV kinetic analysis in the studies of radiation damage and show that chemical ionization and electron excitation are inseparable, but different, mechanisms of radiation damage, which has so far been classified loosely under the single term “ionization.”

High accuracy ab initio potential energy surface for the H2O-H van der Waals dimer.

A representation of the three-dimensional potential energy surface (PES) of the H2O-H van der Waals dimer is presented. The H2O molecule is treated as a rigid body held at its experimentally determined equilibrium geometry, with the OH bond length set to 1.809 650 34 a0 and the HOH bond angle set to 1.824 044 93 radians. Ab initio calculations are carried out at the coupled-cluster single, double, and perturbative triple level, with scalar relativistic effects included using the second-order Douglas-Kroll-Hess approximation. The ab initio calculations employ the aug-cc-pVnZ-DK series of basis sets (n = D, T, Q), which are recontracted versions of the aug-cc-pVnZ basis sets that are appropriate for relativistic calculations. The counterpoise method is used to reduce the basis set superposition error; in addition, results obtained using the aug-cc-pVTZ-DK and aug-cc-pVQZ-DK basis sets were extrapolated to the complete basis set (CBS) limit. The PES is based on calculations carried out at 1054 symmetry-unique H2O-H geometries for which the distance R between the H-atom and the H2O center of mass ranges from R = 2.5-9.0 Å. The reproduction of the PES along the orientational degrees of freedom was performed using Lebedev quadrature and an expansion in spherical harmonics. The mean absolute error of the reproduced PES is <0.02cm-1 for R ≥ 3.0 Å and <0.21cm-1 for R between 2.5 and 3.0 Å. The global minimum for the CBS PES is a coplanar H2O-H geometry, with R = 3.41 Å, in which the angle formed between the H2O C2 symmetry axis and the H-atom is 122.25°; the CBS binding energy for this geometry is 61.297cm-1. In addition, by utilizing the symmetry of the H2O molecule, the spherical harmonic expansion was simplified with no loss in accuracy and a speedup of ∼1.8 was achieved. The reproduced PES can be used in future molecular dynamics simulations.

Quantum-mechanical force balance between multipolar dispersion and Pauli repulsion in atomic van der Waals dimers

The structure and stability of atomic and molecular systems with van der Waals (vdW) bonding are often determined by the interplay between attractive dispersion interactions and repulsive interactions caused by electron confinement. Arising due to different mechanisms -- electron correlation for dispersion and the Pauli exclusion principle for exchange-repulsion -- these interactions do not appear to have a straightforward connection. In this paper, we use a coarse-grained approach for evaluating the exchange energy for two coupled quantum Drude oscillators and investigate the mutual compensation of the attractive and repulsive forces at the equilibrium distance within the multipole expansion of the Coulomb potential. This compensation yields a compact formula relating the vdW radius of an atom to its multipole polarizabilities, $R_{\rm vdW} = A_l^{\,}\, \alpha_l^{{2}/{7(l+1)}}$, where $l$ is the multipole rank and $A_l$ is a conversion factor. Such a relation is compelling because it connects an electronic property of an isolated atom (atomic polarizability) with an equilibrium distance in a dimer composed of two closed-shell atoms. We assess the accuracy of the revealed formula for noble-gas, alkaline-earth, and alkali atoms and show that the $A_l$ can be assumed to be universal constants. Besides a seamless definition of vdW radii, the proposed relation can also be used for the efficient determination of atomic multipole polarizabilities solely based on the corresponding dipole polarizability and the vdW radius. Finally, our work provides a basis for the construction of efficient and minimally-empirical interatomic potentials by combining multipolar interatomic exchange and dispersion forces on an equal footing.

How accurate is the determination of equilibrium structures for van der Waals complexes? The dimer N2O⋯CO as an example.

Plausible methods for accurate determination of equilibrium structures of intermolecular clusters have been assessed for the van der Waals dimer N2O⋯CO. In order to assure a large initial dataset of rotational parameters, we first measured the microwave spectra of the 15N2O⋯12CO and 15N2O⋯13CO isotopologs, expanding previous measurements. Then, an anharmonic force field was calculated ab initio and a semi-experimental equilibrium structure was determined. The dimer structure was also calculated at the coupled-cluster level of theory using very large basis sets with diffuse functions and counterpoise correction. It was found that the contributions of the diffuse functions and the counterpoise correction are not additive and do not compensate each other although they have almost the same value but opposite signs. The semi-experimental and ab initio structures were found to be in fair agreement, with the equilibrium distance between the centers of mass of both monomers being 3.825(13) Å and the intermolecular bond length r(C⋯O) = 3.300(9) Å. In this case, the mass-dependent method did not permit us to determine reliable intermolecular parameters. The combination of experimental rotational constants and results of ab initio calculations thus proves to be very sensitive to examine the accuracy of structural determinations in intermolecular clusters, offering insight into other aggregates.

Magnetic moments of lanthanide van der Waals dimers

Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained in ultracold atom experiments, are investigated. These molecules are known to exhibit a degree of quantum chaos, due to the strong anisotropic mixing of their angular spin and rotation degrees of freedom. Within a model of these molecules, we identify different realms of this anisotropic mixing, depending on whether the spin, the rotation, or both, are significantly mixed by the anisotropy. These realms are in turn generally correlated with the resulting magnetic moments of the states.

Theoretical study of lumichrome, 1-methyl-lumichrome and lumiflavin binding ability with thymine

Abstract Gas-phase geometry and electronic structure of lumichrome, 1-methyl-lumichrome and lumiflavin in the electronic ground state and their excited states were investigated using the Density Functional Theory. Their binding ability with thymine was estimated for model van der Waals dimers with two intermolecular hydrogen bonds. The influence of hydrogen bonds on their photophysical properties was analyzed. Obtained theoretical data were compared with available experimental absorption and fluorescence spectra.

High‐Resolution Electronic Excitation and Emission Spectra of Pentacene and 6,13‐Diazapentacene Monomers and Weakly Bound Dimers by Matrix‐Isolation Spectroscopy

N‐Heteropolycycles are among the most promising candidates for applications in organic devices. For this purpose, a profound understanding of the low‐energy electronic absorbance and emission characteristics is of crucial importance. Herein, we report high‐resolution absorbance and fluorescence spectra of pentacene (PEN) and 6,13‐diazapentacene (DAP) in solid neon obtained using the matrix‐isolation technique. Accompanying DFT calculations allow the assignment of specific vibrationally resolved signals to corresponding modes. Furthermore, we present for the first time evidence for the formation of van der Waals dimers of both substances. These dimers exhibit significantly different optical characteristics resulting from the change of electronic properties evoked by the incorporation of sp2 nitrogen into the molecular backbone.

Exploring photoelectron angular distributions emitted from molecular dimers by two delayed intense laser pulses

We describe the results of experiments and simulations performed with the aim of extending photoelectron spectroscopy with intense laser pulses to the case of molecular compounds. Dimer frame photoelectron angular distributions generated by double ionization of N$_2$-N$_2$ and N$_2$-O$_2$ van der Waals dimers with ultrashort, intense laser pulses are measured using four-body coincidence imaging with a reaction microscope. To study the influence of the first-generated molecular ion on the ionization behavior of the remaining neutral molecule we employ a two-pulse sequence comprising of a linearly polarized and a delayed elliptically polarized laser pulse that allows distinguishing the two ionization steps. By analysis of the obtained electron momentum distributions we show that scattering of the photoelectron on the neighbouring molecular potential leads to a deformation and rotation of the photoelectron angular distribution as compared to that measured for an isolated molecule. Based on this result we demonstrate that the electron momentum space in the dimer case can be separated, allowing to extract information about the ionization pathway from the photoelectron angular distributions. Our work, when implemented with variable pulse delay, opens up the possibility of investigating light-induced electronic dynamics in molecular dimers using angularly resolved photoelectron spectroscopy with intense laser pulses.