TD-CI simulation of the electronic optical response of molecules in intense fields: comparison of RPA, CIS, CIS(D), and EOM-CCSD

A number of different levels of theory have been tested in TD-CI simulations of the response of butadiene interacting with very short, intense laser pulses. Excitation energies and transition dipoles were calculated with linear-response time-dependent Hartree-Fock (also known as the random phase approximation, RPA), configuration interaction in the space of single excitations (CIS), perturbative corrections to CIS involving double excitations [CIS(D)], and the equation-of-motion coupled-cluster (EOM-CC) method using the 6-31G(d,p) basis set augmented with n = 0-3 sets of diffuse sp functions on all carbons and only on the end carbons [6-31 n+ G(d,p) and 6-31(n+)G(d,p), respectively]. Diffuse functions are particularly important for transitions between the pseudocontinuum states above the ionization threshold. Simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. Depending on the basis set, up to 500 excited states were needed for the simulations. Under the conditions selected, the response was too weak with the 6-31G(d,p) basis set, and the difference between levels of theory was more pronounced. When two or three set of diffuse functions were included on all of the carbons, the RPA, CIS, and EOM-CC results were comparable, but the CIS(D) response was too large compared to the more accurate EOM-CC calculations. Even though the frequency of the pulse is not resonant with any of the ground-to-excited transitions, excitations to valence and pseudocontinuum states occur readily above a threshold in the intensity.     

TD-CI simulation of the electronic optical response of molecules in intense fields II: comparison of DFT functionals and EOM-CCSD

Time-dependent configuration interaction (TD-CI) simulations can be used to simulate molecules in intense laser fields. TD-CI calculations use the excitation energies and transition dipoles calculated in the absence of a field. The EOM-CCSD method provides a good estimate of the field-free excited states but is rather expensive. Linear-response time-dependent density functional theory (TD-DFT) is an inexpensive alternative for computing the field-free excitation energies and transition dipoles needed for TD-CI simulations. Linear-response TD-DFT calculations were carried out with standard functionals (B3LYP, BH&HLYP, HSE2PBE (HSE03), BLYP, PBE, PW91, and TPSS) and long-range corrected functionals (LC-ωPBE, ωB97XD, CAM-B3LYP, LC-BLYP, LC-PBE, LC-PW91, and LC-TPSS). These calculations used the 6-31G(d,p) basis set augmented with three sets of diffuse sp functions on each heavy atom. Butadiene was employed as a test case, and 500 excited states were calculated with each functional. Standard functionals yield average excitation energies that are significantly lower than the EOM-CC, while long-range corrected functionals tend to produce average excitation energies slightly higher. Long-range corrected functionals also yield transition dipoles that are somewhat larger than EOM-CC on average. The TD-CI simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. The nonlinear response as indicated by the residual populations of the excited states after the pulse is far too large with standard functionals, primarily because the excitation energies are too low. The LC-ωPBE, LC-PBE, LC-PW91, and LC-TPSS long-range corrected functionals produce responses comparable to EOM-CC.     

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schr?dinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments.     

Lie algebraic approach to multiphoton excitation of diatomic molecules in intense laser fields

The quadratic anharmonic oscillator Lie algebraic model is used to study the multiphoton transition of the diatomic molecule placed in intense laser fields. The multiphoton excitation of vibration and vibration‐rotation of diatomic molecules in intense laser fields are discussed. In the pure vibration transition we calculate the transition probability versus the frequency of the laser fields for the CO molecule. We also investigate the roles of rotational motion in multiphoton processes and compare with pure vibration for the LiH molecule. The influences of the angular quantum number l and the molecular orientations in laser fields on the multiphoton processes are discussed. The averaged absorb energy changing with the laser field's frequency is calculated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 201–207, 1999     

Modification of the velocity distribution of H(2) molecules in a supersonic beam by intense pulsed optical gradients

We report the acceleration and deceleration of H(2) molecules in a supersonic molecular beam by means of its interaction with an intense optical gradient from a nanosecond far-off-resonant optical pulse. The strong optical gradients are formed in the interference pattern of two intense optical pulses at 532 nm. The velocity distribution of the molecular beam, before and after the applied optical pulse, is measured by a velocity-mapped ion imaging technique. Changes in velocity up to 202 m s(-1)+/- 61 m s(-1) are observed in a molecular beam initially travelling at a mean speed of 563 m s(-1). We report the dependence of this change in velocity with the strength of the optical gradient applied.     

Floquet-liouville super-matrix approach for multiphoton non-linear optical processes in intense laser fields

A practical non-perturbative approach is presented for the treatment of multiphoton non-linear optical processes in intense monochromatic or polychromatic field. By extending the many-mode Floquet theory recently developed by the authors, the time-dependent Liouville equation for the density matrix of atoms or molecules undergoing radiative and/or collisional relaxations can be transformed into an equivalent time-independent Floquet-Liouville super-matrix eigenvalue problem. The method is illustrated by a study of the multiphoton resonance fluorescence spectra of two-level systems.     

Electronic,redox, and optical property prediction of organic π-conjugated molecules through a hierarchy of machine learning approaches

Accelerating the development of π-conjugated molecules for applications such as energy generation and storage, catalysis, sensing, pharmaceuticals, and (semi)conducting technologies requires rapid and accurate evaluation of the electronic, redox, or optical properties. While high-throughput computational screening has proven to be a tremendous aid in this regard, machine learning (ML) and other data-driven methods can further enable orders of magnitude reduction in time while at the same time providing dramatic increases in the chemical space that is explored. However, the lack of benchmark datasets containing the electronic, redox, and optical properties that characterize the diverse, known chemical space of organic π-conjugated molecules limits ML model development. Here, we present a curated dataset containing 25k molecules with density functional theory (DFT) and time-dependent DFT (TDDFT) evaluated properties that include frontier molecular orbitals, ionization energies, relaxation energies, and low-lying optical excitation energies. Using the dataset, we train a hierarchy of ML models, ranging from classical models such as ridge regression to sophisticated graph neural networks, with molecular SMILES representation as input. We observe that graph neural networks augmented with contextual information allow for significantly better predictions across a wide array of properties. Our best-performing models also provide an uncertainty quantification for the predictions. To democratize access to the data and trained models, an interactive web platform has been developed and deployed.

A hierarchical series of machine learning models are developed to provide robust predictions of the electronic, redox, and optical properties of π-conjugated molecules.     

Classical dynamics of 3D Hydrogen molecular ion in intense laser fields

The classical trajectory method is used to study the dynamics of 3D Hydrogen molecular ion interacting with intense laser fields. In the 3D classical model, a three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser field is considered. The motion of electron and nucleus is described by the classical Hamiltonian canonical equations. The probabilities of ionization, dissociation and Coulomb explosion as functions of time are calculated and the average distances from electron to the mass-center for various laser parameters are implemented by symplectic method. The dynamics of in two-color laser fields are also investigated. We compare our results with the corresponding quantum-mechanical calculations and find they produce similar qualitative features in many cases.     

Electronic structure and optical properties of chelating heteroatomic conjugated molecules: a SAC-CI study

The electronic structure and optical properties of 13 chelating heteroatomic conjugated molecules such as pyridine, benzoxazole, and benzothiazole derivatives, which are used as C–N ligands in organometallic compounds, have been investigated. The geometries of the ground and first excited states were obtained by the DFT and CIS methods, respectively, followed by the SAC-CI calculations of the transition energies for absorption and emission. For six compounds whose experimental data are available, the SAC-CI calculations reproduced the experimental values satisfactorily with deviations of less than 0.3 eV for absorption and 0.1 eV for emission except for benzoxazoles. For other molecules, the theoretical absorption and emission spectra were predicted. The lowest ππ* excited-state geometries was calculated to be planar for most of the molecules with two or three conjugated rings connected by single bond. The geometry change due to the ππ* excitation was qualitatively interpreted by electrostatic force theory based on SAC/SAC-CI electron density difference. The excitations are relatively localized in the central region and in the lowest ππ* excited state, the inter-ring single bond shows large change, with a contraction of 0.05–0.09 Å. The present calculations provide reliable information regarding the energy levels of these chelating heteroatomic conjugated compounds.     

Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: an ab initio electronic state study

A theory of quantum electron wavepacket dynamics that nonadiabatically couples with classical nuclear motions in intense optical fields is studied. The formalism is intended to track the laser-driven electron wavepackets in terms of the linear combination of configuration-state functions generated with ab initio molecular orbitals. Beginning with the total quantum Hamiltonian for electrons and nuclei in the vector potential of classical electromagnetic field, we reduce the Hamiltonian into a mixed quantum-classical representation by replacing the quantum nuclear momentum operators with the classical counterparts. This framework gives equations of motion for electron wavepackets in an intense laser field through the time dependent variational principle. On the other hand, a generalization of the Newtonian equations provides a matrix form of forces acting on the nuclei for nonadiabatic dynamics. A mean-field approximation to the force matrix reduces this higher order formalism to the semiclassical Ehrenfest theory in intense optical fields. To bring these theories into a practical quantum chemical package for general molecules, we have implemented the relevant ab initio algorithms in it. Some numerical results in the level of the semiclassical Ehrenfest-type theory with explicit use of the nuclear kinematic (derivative) coupling and the velocity form for the optical interaction are presented.     

Flow birefringence and optical anisotropy of poly(N-vinylpyrrolidone) molecules

Concentration dependences of flow birefringence and viscosity of poly(N-vinylpyrrolidone) solutions in water and benzyl alcohol are investigated. The intrinsic anisotropy for a poly(N-vinylpyrrolidone) macromolecular segment, (α₁ ? α₂) = ?(82 ± 8) × 10^?25 cm³, is determined from the results of birefringence measurements in benzyl alcohol. For aqueous solutions, a strong concentration dependence of the specific anisotropy of solution is obtained, a result that may be explained by the heterogeneity of coils. A model allowing for this heterogeneity is suggested. It makes it possible to fit the concentration dependence to a hyperbolic function, to separate contributions of heterogeneity anisotropy and form anisotropy to the birefringence of a solution, and to estimate the segment asymmetry parameter as p = 3.0 ± 0.5.     

Phenanthrenequinone adsorbed on Si(001): geometries, electronic properties, and optical response

As a prototypical case of a pi-conjugated organic overlayer on a semiconductor surface the adsorption of phenanthrenequinone (C14O2H8) on the Si(001) surface is studied by means of first principles calculations, using gradient-corrected density functional theory together with ultrasoft pseudopotentials and the projector augmented wave method. A thermodynamic phase diagram gives adsorption geometries depending on experimental conditions, the microscopically most favorable bonding configuration representing a "[4+2]-cycloaddition product". The surface electronic structure depends strongly on the respective adsorption configuration. Calculations of the surface optical signature show its sensitivity to molecular adsorption and are in agreement with experimental results. A detailed analysis illustrates that the bonding to the surface has to be taken into account accurately to unveil the molecule's contribution to the surface optical response.     

Time-dependent multiconfiguration theory for electronic dynamics of molecules in intense laser fields: a description in terms of numerical orbital functions

The equations of motion (EOMs) for spin orbitals in the coordinate representation are derived within the framework of the time-dependent multiconfiguration theory developed for electronic dynamics of molecules in intense laser fields. We then tailor the EOMs for diatomic (or linear) molecules to apply the theory to the electronic dynamics of a hydrogen molecule in an intense, near-infrared laser field. Numerical results are presented to demonstrate that the time-dependent numerical multiconfiguration wave function is able to describe the correlated electron motions as well as the ionization processes of a molecule in intense laser fields.     

Ionization process of the hydrogen atom in intense laser fields: Non–Born-Oppenheimer 1D model calculations

The ionization process of the hydrogen atom in two-color laser field is investigated based on non–Born-Oppenheimer one-dimensional model. In this model, both electron and nucleus are described by the time-dependent Hartree equations. By numerically solving the equations, the influence of the relative phase ϕ of the laser field with the spatial distribution of electron and nucleus is investigated. For ϕ = 0, the electron is moved to the direction in which the maximum of the asymmetric combined electric field pointed. For ϕ = π/2, the electron is shown to be pulled in the opposite direction. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Electronic structure, X-ray absorption, and optical spectroscopy of LaCoO(3) in the ground-state and excited-states

We present the magnetic and optical properties of various combinations of ordered spin state configurations between low-spin (LS) state, intermediate-spin (IS) state, and high-spin (HS) state of LaCoO(3) . In this study, we use the state-of-the-art first principles calculations based on generalized gradient (GGA) + Hubbard U approach. The excited-state properties of different spin configurations of LaCoO(3) such as the X-ray absorption spectra, optical conductivity, reflectivity, and electron energy loss are calculated. We have demonstrated that the optical spectra results can be used for analyzing the spin state of Co(3+) ion. The first specie is the local excitation of IS cobalt ions in the LS ground state. The second excitation leads to the stabilization of the mixed IS/HS Co(3+) metallic state. At low temperature, the comparison between O 2p and Co 3d projected density of states with the experimental valence band spectra indicates significant IS Co(3+) ions and this is in sharp contrast to the HS state which is negligible. The line shape of O 2s and Co 3d core level spectra are well reproduced in this study. The present results are in excellent agreement with the available experimental data. The variation in the spectra of different configurations of LaCoO(3) suggests a changing in the spin state as the temperature is enhanced from 90 to 500 K.     

Electronic structure and nonlinear optical properties of push–pull conjugated molecules

We present a review of ab initio calculations we recently performed on organic molecules presenting promising quadratic nonlinear optical properties. These molecules constitute so-called push–pull conjugated compounds in which a conjugated segment is capped at one end by an acceptor group and at the other end by a donor group. We foucs on three series of systems: (i) p-amino-p′-nitrodiphenylacetylenes for which “unusual” distorsion patterns have been recently reported; (ii) benzodithiapolyenals, which present among the largest second-order polarizabilities ever measured; and (iii) 2-methylene-2H-pyrrole derivatives. Our results are found to provide a detailed understanding of the avilable experimental data.     

Discrete variable approaches to tetratomic molecules: part I: DVR(6) and DVR(3) + DGB methods

We present two discrete variable representation (DVR) based methods for the determination of the vibrational energy levels of tetratomic molecules. Both methods are designed for orthogonal internal coordinates in a body-fixed reference frame and make use of the DVR of three angular variables. The angular DVRs allow the construction of a fixed-angle three-mode Hamiltonian for the stretching vibrations. For each of the angular triples, the stretching eigenvalue problems are solved by employing 3D radial DVRs in the DVR(6) approach and real three-dimensional distributed Gaussian functions in the DVR(3) + DGB method. The angular degrees of freedom are taken sequentially into account in conjunction with a contraction scheme resulting from several diagonalization/truncation steps. Vibrationally averaged geometries, expectation values of rotational constants, and several adiabatic projection schemes developed in this work for tetratomic molecules are used to characterize the vibrational levels calculated by the DVR(6) and DVR(3) + DGB.     

Electronic excited states of Si(100) and organic molecules adsorbed on Si(100)

The electronically excited states of the Si(100) surface and acetylene, benzene, and 9,10-phenanthrenequinone adsorbed on Si(100) are studied with time-dependent density functional theory. The computational cost of these calculations can be reduced through truncation of the single excitation space. This allows larger cluster models of the surface in conjunction with large adsorbates to be studied. On clean Si(100), the low-lying excitations correspond to transitions between the pi orbitals of the silicon-silicon dimers. These excitations are predicted to occur in the range 0.4-2 eV. When organic molecules are adsorbed on the surface, surface --> molecule, molecule --> surface, and electronic excitations localized within the adsorbate are also observed at higher energies. For acetylene and benzene, the remaining pipi* excitations are found to lie at lower energies than in the corresponding gas-phase species. Even though the aromaticity of 9,10-phenanthrenequinone is retained, significant shifts in the pipi* excitations of the aromatic rings are predicted. This is in part due to structural changes that occur upon adsorption.     

Synthesis, characterization, and optical response of dipolar and non-dipolar poly(phenylenevinylene) dendrimers

New dipolar and non-dipolar poly(phenylenevinylene) dendrimers bearing electron-donating and electron-withdrawing groups have been efficiently synthesized using Heck and Horner-Wadsworth-Emmons reactions. The photoluminescence of these systems may be tuned in the blue zone by choosing the appropriate peripheral groups. Despite the meta-substitution pattern, large Stokes shifts can be observed when pi-donor and pi-acceptor groups are connected by a m-phenylenevinylene system.     

Electronic degeneracies in symmetric (Jahn-Teller) and nonsymmetric aliphatic radical cations: global topology of sigma-bonded molecules

The ground-state potential surfaces of five aliphatic radical cations are investigated using a spin-pairing model. It is shown that the ground-state surface of an n-atomic system supports several stationary points (minima and transition states, including second-order ones). In addition, there are numerous nuclear configurations at which the ground state is electronically degenerate. The electronic degeneracies due to interactions between atoms bound to the same atom are either 2-fold (conical intersections) or 3-fold degenerate but not of a higher dimension. Each 3-fold degeneracy is accompanied by an even number of conical intersections (four or two). A systematic procedure for locating all of these nuclear configurations (that are in fact 3n - 8 or 3n - 11 dimensional hypersurfaces) is described. The model allows for the qualitative determination of the structure and charge distribution of the system at all of the stationary points and electronic degeneracies. Quantum chemical calculations confirm the predictions of the model, which is used to direct and facilitate the calculations.