The Dalton quantum chemistry program system

Two-photon isomerization properties of donor-acceptor Stenhouse adducts

Donor-acceptor Stenhouse adducts (DASAs) are important photo-responsive molecules that undergo electrocyclic reactions after light absorption. From these properties, DASAs have received extensive attention as photo-switches with negative photochromism. Meanwhile, several photochemical applications require isomerization events to take place in highly localized volumes at variable depths. Such focused photoreactions can be achieved if the electronic excitation is induced through a non-linear optical process. In this contribution we describe DASAs substituted with extended donor groups which provide them with significant two-photon absorption properties. We characterized the photo-induced transformation of these DASAs from the open polymethinic form to their cyclopentenic isomer with the use of 800 nm femtosecond pulses. These studies verified that the biphotonic excitation produces equivalent photoreactions as linear absorbance. We also determined these DASAs' two-photon absorption cross sections from measurements of their photoconverted yield after biphotonic excitation. As we show, specific donor sections provide these systems with important biphotonic cross-sections as high as 615 GM units. Such properties make these DASAs among the most non-linearly active photo-switchable molecules. Calculations at the TDDFT level with the optimally tuned range-separated functional OT-CAM-B3LYP, together with quadratic response methods indicate that the non-linear photochemical properties in these molecules involve higher lying electronic states above the first excited singlet. This result is consistent with the observed relation between their two-photon chemistry and the onset of their short wavelength absorption features around 400 nm. This is the first report of the non-linear photochemistry of DASAs. The two-photon isomerization properties of DASAs extend their applications to 3D-photocontrol, non-linear lithography, variable depth birefringence, and localized drug delivery schemes.

Complete Active Space Methods for NISQ Devices: The Importance of Canonical Orbital Optimization for Accuracy and Noise Resilience

To avoid the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive regions, which is also known as complete active space methods. However, selecting the active space alone is not enough to accurately describe quantum mechanical effects such as correlation. This study emphasizes the importance of optimizing the active space orbitals to describe correlation and improve the basis-dependent Hartree-Fock energies. We will explore classical and quantum computation methods for orbital optimization and compare the chemically inspired ansatz, UCCSD, with the classical full CI approach for describing the active space in both weakly and strongly correlated molecules. Finally, we will investigate the practical implementation of a quantum CASSCF, where hardware-efficient circuits must be used and noise can interfere with accuracy and convergence. Additionally, we will examine the impact of using canonical and noncanonical active orbitals on the convergence of the quantum CASSCF routine in the presence of noise.

New pecJ-n (n = 1, 2) Basis Sets for Selenium Atom Purposed for the Calculations of NMR Spin-Spin Coupling Constants Involving Selenium

We present new compact pecJ-n (n = 1, 2) basis sets for the selenium atom developed for the quantum-chemical calculations of NMR spin-spin coupling constants (SSCCs) involving selenium nuclei. These basis sets were obtained at the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) level with the property-energy consistent (PEC) method, which was introduced in our previous papers. The existing SSCC-oriented selenium basis sets are rather large in size, while the PEC method gives more compact basis sets that are capable of providing accuracy comparable to that reached using the property-oriented basis sets of larger sizes generated with a standard even-tempered technique. This is due to the fact that the PEC method is very different in its essence from the even-tempered approaches. It generates new exponents through the total optimization of angular spaces of trial basis sets with respect to the property under consideration and the total molecular energy. New basis sets were tested on the coupled cluster singles and doubles (CCSD) calculations of SSCCs involving selenium in the representative series of molecules, taking into account relativistic, solvent, and vibrational corrections. The comparison with the experiment showed that the accuracy of the results obtained with the pecJ-2 basis set is almost the same as that provided by a significantly larger basis set, aug-cc-pVTZ-J, while that achieved with a very compact pecJ-1 basis set is only slightly inferior to the accuracy provided by the former.

Efficient calculation of derivatives of integrals in a basis of non-separable Gaussians

A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations. The approach, based on symbolic computation with computer algebra systems and automated generation of optimized subroutines, takes full advantage of sparsity and is here applied to first energy derivatives with respect to nuclear displacements and lattice parameters of molecules and materials. The implementation in the Crystal code is presented, and the considerably improved computational efficiency over the previous implementation is illustrated. For this purpose, three different tasks involving the use of analytical forces are considered: (i) geometry optimization; (ii) harmonic frequency calculation; and (iii) elastic tensor calculation. Three test case materials are selected as representatives of different classes: (i) a metallic 2D model of the Cu(111) surface; (ii) a wide-gap semiconductor ZnO crystal, with a wurtzite-type structure; and (iii) a porous metal-organic crystal, namely the ZIF-8 zinc-imidazolate framework. Finally, it is argued that the present symbolic approach is particularly amenable to generalizations, and its potential application to other derivatives is sketched.

Adiabatic extraction of nonlinear optical properties from real-time time-dependent electronic-structure theory

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability.

Magnetic dipole and quadrupole transitions in the ν2 + ν3 vibrational band of carbon dioxide

This paper aims at the theoretical study of the CO₂ magnetic-dipole ν₂ + ν₃ rovibrational absorption band that was recently detected in the Martian atmosphere. Specific characteristics of the magnetic dipole operator are carefully examined. Our evaluation of the magnetic-dipole line intensities is based on the variational calculations and the use of molecular properties is determined through specially performed ab initio quantum chemical calculations. The comparison of our simulated magnetic-dipole spectrum with available laboratory taken data also requires the knowledge of line intensities in the quadrupole band, which partially overlaps with that magnetic-dipole. Quadrupole intensities, once reconsidered, are permitted to correct previously reported values of the integrated intensity as well as the intensity of selected branches. The sum of our calculated magnetic-dipole and quadrupole rovibrational lines is shown to be in good agreement with both sets of presently available data from FTIR and OFCEAS laboratory observations.

Curing the Divergence in Time-Dependent Density Functional Quadratic Response Theory

The adiabatic approximation in time-dependent density functional theory is known to give an incorrect pole structure in the quadratic response function, leading to unphysical divergences in excited state-to-state transition probabilities and hyperpolarizabilties. We find the form of the exact quadratic response kernel and derive a practical and accurate approximation that cures the divergence. We demonstrate our results on excited state-to-state transition probabilities of a model system and of the LiH molecule.

Embedding Beyond Electrostatics: The Extended Polarizable Density Embedding Model

The polarizable density embedding (PDE) model is a focused QM/QM fragment-based embedding model designed to model solvation effects on molecular properties. We extend the PDE model to include exchange and nonadditive exchange-correlation (for DFT) in the embedding potential in addition to the existing electrostatic, polarization, and nonelectrostatic effects already present. The resulting model, termed PDE-X, yields localized electronic excitation energies that accurately capture the range dependence of the solvent interaction and gives close agreement with full quantum mechanical (QM) results, even when using minimal QM regions. We show that the PDE-X embedding description consistently improves the accuracy of excitation energies for a diverse set of organic chromophores. The improved embedding description leads to systematic solvent effects that do not average out when applying configurational sampling.

On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

Theoretical Investigation of Ru(II) Complexes with Long Lifetime and a Large Two-Photon Absorption Cross-Section in Photodynamic Therapy

Two-photon photodynamic therapy (TP-PDT), as a new method for cancer, has shown unique advantages in tumors. A low two-photon absorption cross-section (δ) in the biologic spectral window and a short triplet state lifetime are the important issues faced by the current photosensitizers (PSs) in TP-PDT. In this paper, the photophysical properties of a series of Ru(II) complexes were studied by density functional theory and time-dependent density functional theory methods. The electronic structure, one- and two-photon absorption properties, type I/II mechanisms, triplet state lifetime, and solvation free energy were calculated. The results showed that the substitution of methoxyls by pyrene groups greatly improved the lifetime of the complex. Furthermore, the addition of acetylenyl groups subtly enhanced δ. Overall, complex 3b possess a large δ(1376 GM), a long lifetime (136 μs), and better solvation free energy. It is hoped that it can provide valuable theoretical guidance for the design and synthesis of efficient two-photon PSs in the experiment.

Induction effects on the absorption maxima of photoreceptor proteins

Multiscale simulations have been established as a powerful tool to calculate and predict excitation energies in complex systems such as photoreceptor proteins. In these simulations the chromophore is typically treated using quantum mechanical (QM) methods while the protein and surrounding environment are described by a classical molecular mechanics (MM) force field. The electrostatic interactions between these regions are often treated using electrostatic embedding where the point charges in the MM region polarize the QM region. A more sophisticated treatment accounts also for the polarization of the MM region. In this work, the effect of such a polarizable embedding on excitation energies was benchmarked and compared to electrostatic embedding. This was done for two different proteins, the lipid membrane-embedded jumping spider rhodopsin and the soluble cyanobacteriochrome Slr1393g3. It was found that the polarizable embedding scheme produces absorption maxima closer to experimental values. The polarizable embedding scheme was also benchmarked against expanded QM regions and found to be in qualitative agreement. Treating individual residues as polarizable recovered between 50% and 71% of the QM improvement in the excitation energies, depending on the system. A detailed analysis of each amino acid residue in the chromophore binding pocket revealed that aromatic residues result in the largest change in excitation energy compared to the electrostatic embedding. Furthermore, the computational efficiency of polarizable embedding allowed it to go beyond the binding pocket and describe a larger portion of the environment, further improving the results.

Collision-induced three-body polarizability of helium

We present the first-principles determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster and full configuration interaction methods were used to perform electronic structure calculations. The mean absolute relative uncertainty of the trace of the polarizability tensor, resulting from the incompleteness of the orbital basis set, was found to be 4.7%. Additional uncertainty due to the approximate treatment of triple and the neglect of higher excitations was estimated at 5.7%. An analytic function was developed to describe the short-range behavior of the polarizability and its asymptotics in all fragmentation channels. We calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations [Garberoglio et al., J. Chem. Phys. 155, 234103 (2021)] employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K, we observed a significant discrepancy between the classical results obtained using superposition approximation and the ab initio computed polarizability. For temperatures from 10 K up to 200 K, the differences between PIMC and semiclassical calculations are several times smaller than the uncertainties of our results. Except at low temperatures, our results agree very well with the available experimental data but have much smaller uncertainties. The data reported in this work eliminate the main accuracy bottleneck in the optical pressure standard [Gaiser et al., Ann. Phys. 534, 2200336 (2022)] and facilitate further progress in the field of quantum metrology.

Benchmarking two-photon absorption strengths of rhodopsin chromophore models with CC3 and CCSD methodologies: An assessment of popular density functional approximations

This work presents the investigations of the impact of an increasing electron correlation in the hierarchy of coupled-cluster methods, i.e., CC2, CCSD, and CC3, on two-photon absorption (2PA) strengths for the lowest excited state of the minimal rhodopsin's chromophore model-cis-penta-2,4-dieniminium cation (PSB3). For a larger chromophore's model [4-cis-hepta-2,4,6-trieniminium cation (PSB4)], CC2 and CCSD calculations of 2PA strengths were performed. Additionally, 2PA strengths predicted by some popular density functional theory (DFT) functionals differing in HF exchange contribution were assessed against the reference CC3/CCSD data. For PSB3, the accuracy of 2PA strengths increases in the following order: CC2 < CCSD < CC3, with the CC2 deviation from both higher-level methods exceeding 10% at 6-31+G* basis sets and 2% at aug-cc-pVDZ basis set. However, for PSB4, this trend is reversed and CC2-based 2PA strength is larger than the corresponding CCSD value. Among the DFT functionals investigated, CAM-B3LYP and BHandHLYP provide 2PA strengths in best compliance with reference data, however, with the error approaching an order of magnitude.

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited ¹Δ_g state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for ¹L_a and ¹L_b states in polyacenes and ¹A_u and ¹A_g states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

Computational NMR of carbohydrates: 1. Glucopyranoses

A high-level calculation of ¹ H and ¹³ C NMR chemical shifts of α- and β-d-glucopyranoses is carried out at the DFT level with taking into account their conformational composition to reveal the most effective computational protocols. A number of dedicated DFT functionals in combination with Jensen's pcS-n (n = 0-4) family of basis sets were applied to evaluate the most reliable combination. It was found that BHandHLYP/pcS-2 provided the most accurate and reliable computational protocol. Based on the performed calculations, the established computational protocol is generally recommended for the calculation of ¹ H and ¹³ C NMR chemical shifts of a wide series of carbohydrates.

Theoretical study on the origin of the dual phosphorescence emission from organic aggregates at room temperature

Purely organic materials with dual room temperature phosphorescence (RTP) phenomenon were reported recently, but the underlying mechanism was still ambiguous. Herein, we revealed the source of dual RTP emission, taking CzDPS crystal as prototype, by using hybrid quantum mechanics and molecular mechanics (QM/MM) coupled with the thermal vibration correlation function rate theory. Theoretical calculations verified that the emission lifetimes are prolonged from 70 ms in the higher triplet state T₂ to 216 ms in the lowest triplet state T₁, which is well consistent with the increase of RTP lifetimes from 74 ms for the peak at 465 nm to 627 ms for the band at 565 nm. This is because the radiative and nonradiative decay rates are larger for T₂ → S₀ than that of T₁ → S₀, which was mainly contributed by the synergistic effect of the increase of spin-orbit coupling and excitation energy, as well as the decrease of reorganization energy. Moreover, the simulated RTP spectra agree well with the experimental ones, including the emission position and profiles. Therefore, the upper-lying triplet excited states are responsible for the dual RTP in CzDPS crystal. This work could contribute to further understanding on the multiple luminescence of organic aggregates.

Frequency-resolved microscopic second-order hyperpolarizability of azochromophores: a study on nonlinear all-optical switching applications

Azochromophores present interesting optical properties for application in all-optical switches (AOSs), such as ultrafast photoisomerization and considerable nonlinear optical response. However, determining the frequency-resolved microscopic second-order hyperpolarizability (real and imaginary parts) related to the pure electronic effects of molecules in solution is a challenging task. In this context, we have used femtosecond-laser induced nonlinear ellipse rotation (NER) measurements to obtain the electronic nonlinear refraction (n₂(ω)) and two-photon absorption spectra (α_2PA(ω)) of four azochromophores dissolved in methanol and acetone. The measurements ranging from ∼600 up to ∼1300 nm were performed in Disperse Red 1 (DR1), Disperse Red 13 (DR13), Disperse Red 19 (DR19), and Disperse Orange 3 (DO3). Because we carried the solution in a silica cuvette and used a short focal length, we were able to measure the solution's nonlinearities with high precision, as the silica from the cuvette walls worked as a suitable reference medium. Consequently, we precisely determined n₂(ω), α_2PA(ω), and the second-order hyperpolarizability (γ(ω)) for all molecules and explained the different magnitudes based on the push-pull character. Furthermore, the solvation effect due to the change from methanol to acetone solvent on the n₂(ω), α_2PA(ω), and γ(ω) is also reported. The results were elucidated using the sum-over-states (SOS) approach within the few-energy-level model and the results were obtained via quantum-chemical calculations using the cubic response function formalism within the density functional theory framework. Finally, we used these results to determine the frequency-resolved figure-of-merit for all-optical switching applications. Our results suggest that chromophores have the potential for applications in AOS based on Fabry-Perot filters.

Model systems for dye-sensitized solar cells: cyanidin-silver nanocluster hybrids at TiO2 support

Theoretical study of structural, optical, and photovoltaic properties of novel bio-nano hybrids (dye-nanocluster), as well as at TiO2 surface model support is presented in the context of the application for dye-sensitized solar cells (DSSC). A group of anthocyanidin dyes (pelargonidin, cyanidin, delphinidin, peonidin, petunidin, and malvidin) represented by cyanidin covalently bound to silver nanoclusters (NCs) with even or odd number of valence electrons have been investigated using DFT and TDDFT approach. The key role of nanoclusters as acceptors in hybrids cyanidin-NC has been shown. The nanoclusters with an even number of valence electrons are suitable as acceptors in hybrids. The interaction of bio-nano (cyanidin-NC) hybrid with the TiO2 surface model has been investigated in the context of absorption in near-infrared (NIR) and charge separation due to donor and acceptor subunits. Altogether, the theoretical concept serves to identify the key steps in the design of novel solar cells based on bio-nano hybrids at TiO2 surface for DSSC application.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S₁) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

Unified Description of Proton NMR Relaxation in Water, Acetonitrile, and Methane from Molecular Dynamics Simulations in the Liquid, Supercritical, and Gas Phases

A comprehensive calculation of proton NMR relaxation in water, acetonitrile, and methane across a wide range of the phase diagram is provided via ab initio and force-field-based molecular dynamics simulations. The formalism used for the spin-rotation (SR) contribution to relaxation is developed for use with any molecular symmetry and utilizes the full molecular SR tensors, which are calculated from first-principles via Kohn-Sham (KS) DFT. In combination with calculations of the dipolar contribution, near-quantitative agreement with total measured relaxation rates is achieved.

Theory, implementation, and disappointing results for two-photon absorption cross sections within the doubly electron-attached equation-of-motion coupled-cluster framework

The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels.

FCclasses3: Vibrationally-resolved spectra simulated at the edge of the harmonic approximation

We introduce FCclasses3, a code to carry out vibronic simulations of electronic spectra and nonradiative rates, based on the harmonic approximation. Key new features are: implementation of the full family of vertical and adiabatic harmonic models, vibrational analysis in curvilinear coordinates, extension to several electronic spectroscopies and implementation of time-dependent approaches. The use of curvilinear valence internal coordinates allows the adoption of quadratic model potential energy surfaces (PES) of the initial and final states expanded at arbitrary configurations. Moreover, the implementation of suitable projectors provides a robust framework for defining reduced-dimensionality models by sorting flexible coordinates out of the harmonic subset, so that they can then be treated at anharmonic level, or with mixed quantum classical approaches. A set of tools to facilitate input preparation and output analysis is also provided. We show the program at work in the simulation of different spectra (one and two-photon absorption, emission and resonance Raman) and internal conversion rate of a typical rigid molecule, anthracene. Then, we focus on absorption and emission spectra of a series of flexible polyphenyl molecules, highlighting the relevance of some of the newly implemented features. The code is freely available at http://www.iccom.cnr.it/en/fcclasses/.

Ultrafast Excited State Aromatization in Dihydroazulene

Excited-state aromatization dynamics in the photochemical ring opening of dihydroazulene (DHA) is investigated by nonadiabatic molecular dynamics simulations in connection with the mixed-reference spin-flip (MRSF)-TDDFT method. It is found that, in the main reaction channel, the ring opening occurs in the excited state in a sequence of steps with increasing aromaticity. The first stage lasting ca. 200 fs produces an 8π semiaromatic S₁ minimum (S_1, min) through an ultrafast damped bond length alternation (BLA) movement synchronized with a partial planarization of the cycloheptatriene ring. An additional ca. 200 fs are required to gain the vibrational energy needed to overcome a ring-opening transition state characterized by an enhanced Baird aromaticity. Unlike other BLA motions of ππ* state, it was shown that their damping is a characteristic feature of aromatic bond-equalization process. In addition, some minor channels of the reaction have also been discovered, where noticeably higher barriers of the S₁ non/antiaromatic transition structures must be surmounted. These anti-Baird channels led to reformation of DHA or other closed-ring products. The observed competition between the Baird and anti-Baird channels suggests that the quantum yield of photochemical products can be controllable by tipping their balance. Hence, here we suggest including the concept of anti-Baird, which would expand the applicability of Baird rule to much broader situations.

Magnetic Shielding Analysis of Bonding in [1.1.1]Propellane

The bonding in [1.1.1]propellane, bicyclo[1.1.0]butane, bicyclo[1.1.1]pentane, tetrahedrane, and cyclopropane is investigated by analyzing changes in the off-nucleus isotropic magnetic shielding within the space surrounding each of these molecules and, for [1.1.1]propellane, by examining also the diamagnetic and paramagnetic contributions to this shielding. Any shielding arising from the two "exo" sp³-like hybrid atomic orbitals on the bridgehead carbon atoms that have been used to support the idea of an inverted bond between these two atoms is found to be almost entirely contained within the [1.1.1]propellane cage and to contribute to a strongly shielded central region. This strongly shielded region suggests the establishment of a mainly covalent bonding interaction involving all carbon atoms that cannot be straightforwardly decomposed into contributions from individual carbon-carbon bonds. The emergence of the strongly shielding central region is traced by comparing the shielding variations in and around molecules with one three-membered carbon ring (cyclopropane), two fused three-membered carbon rings (bicyclo[1.1.0]butane), and three fused three-membered carbon rings ([1.1.1]propellane).

Development of accurate potentials for the physisorption of water on graphene

From coupled-cluster singles and doubles model including connected triples corrections [CCSD(T)] calculations on the water dimer and B97D/CC on the water-circumcoronene complex at a large number of randomly generated conformations, interaction potentials for the physisorption of water on graphene are built, accomplishing almost sub-chemical accuracy. The force fields were constructed by decomposing the interaction into electrostatic and van der Waals contributions, the latter represented through improved Lennard-Jones potentials. Besides, a Chemistry at Harvard Macromolecular Mechanics (CHARMM)-like term was included in the water-water potential to improve the description of hydrogen bonds, and an induction term was added to model the polarization effects in the interaction between water and polyaromatic hydrocarbons (PAHs) or graphene. Two schemes with three and six point charges were considered for the interactions water-water and water-PAH, as Coulomb contributions are zero in the water-graphene system. The proposed fitted potentials reproduce the ab initio data used to build them in the whole range of distances and conformations and provide results for selected points very close to CCSD(T) benchmarks. When applied to the water-graphene system, the obtained results are in excellent agreement with p-CCSD(T), revised symmetry-adapted perturbation theory based on density functional theory monomer properties (DFT-SAPT), and diffusion Monte Carlo reference values. Furthermore, the stability of the various conformers water-PAH and water-graphene, as well as the different trends observed between these systems are rationalized in terms of the modifications of the electrostatic contribution.

Multiscale Modeling Unravels the Influence of Biomembranes on the Photochemical Properties of Embedded Anti-Oxidative Polyphenolic and Phenanthroline Chelating Dyes

The embedding of caffeate methyl ester, the flavonoids luteolin and quercetin, and the o-phenanthroline and neocuproine in a liquid disordered lipid bilayer has been studied through extensive atomistic calculations. The location and the orientation of these bio-active antioxidants are explained and analyzed. While the two phenanthrolines strongly associate with the lipid tail region, the other three compounds are rather found among the head groups. The simulations showcase conformational changes of the flavonoids. Through the use of a hybrid quantum mechanics-molecular mechanics scheme and supported by a profound benchmarking of the electronic excited-state method for these compounds, the influence of the anisotropic environment on the compounds' optical properties is analyzed. Influences of surrounding water molecules and of the polar parts of the lipids on the transition dipole moments and excited-state dipole moments are weighted with respect to a change in conformation. The current study highlights the importance of the mapping of molecular interactions in model membranes and pinpoints properties, which can be biomedically used to discriminate and detect different lipid environments.

GA, Jensen SR, Eikås RDR, Frediani L. MRChem Multiresolution Analysis Code for Molecular Electronic Structure Calculations: Performance and Scaling Properties

MRChem is a code for molecular electronic structure calculations, based on a multiwavelet adaptive basis representation. We provide a description of our implementation strategy and several benchmark calculations. Systems comprising more than a thousand orbitals are investigated at the Hartree-Fock level of theory, with an emphasis on scaling properties. With our design, terms that formally scale quadratically with the system size in effect have a better scaling because of the implicit screening introduced by the inherent adaptivity of the method: all operations are performed to the requested precision, which serves the dual purpose of minimizing the computational cost and controlling the final error precisely. Comparisons with traditional Gaussian-type orbitals-based software show that MRChem can be competitive with respect to performance.

High order relativistic corrections on the electric field gradient within the LRESC formalism

In this work, we present relativistic corrections to the electric field gradient (EFG) given by the Linear Response Elimination of the Small Component (LRESC) scheme at 1/c² order and including for the first time spin-dependent (SD) corrections at 1/c⁴ order. We show that these new terms improve the performance of LRESC as results with this methodology are very close to those calculated at the four-component Dirac-Hartree-Fock (4c-DHF) level. We assess the new corrections in BrY and AtY di-halogen (Y = F, Cl, Br, I, and At) and XZY bi-linear molecules (Z = Zn, Cd, and Hg; X, Y = F, Cl, Br, I, and At). At the 4c-DHF level, we analyze the contributions coming from the large and small components of the relativistic 4c wave function to the electronic part of EFG and compare them with the LRESC corrections to find their electronic origin. For the HgX₂ (X = Cl, Br, and I) subset, when the SD correcting terms are included, LRESC calculations match very well with 4c-DHF ones and those from the literature, with differences less than 1% for molecules containing up to three heavy atoms. We show that LRESC gives accurate values of EFG, allowing the analysis of the electronic origin of relativistic effects in terms of well-known nonrelativistic operators.

Research and Design of Aggregation-Induced Phosphorescent Materials for Time-Resolved Two-Photon Excited Luminescence Imaging

Pure organic two-photon excited room temperature phosphorescent (RTP) materials have attracted great attention for time-resolved imaging due to their long emission lifetime and high resolution. The materials with an aromatic carbonyl group exhibit aggregation-induced emission (AIE) and RTP characteristics simultaneously. Here, we deeply explored the nature of aggregation-induced phosphorescence (AIP), especially the relationship between molecular configuration and optical properties. It was found that aggregation effect can suppress geometrical vibrations and regulate energy difference between S₁ and T₁. The aromatic carbonyl group plays significant roles in changing electronic configuration, resulting in large Stokes shift and spin-orbit coupling. It also leads to small transition dipole moment, decreasing two-photon absorption cross section and radiative decay rate. To improve two-photon absorption properties, we further designed a π-conjugated compound with large two-photon absorption cross section in the biological window (36.40 GM/656 nm) and AIP characteristics, which is a potential material in the application of time-resolved two-photon excited imaging.

Competition between ultralong organic phosphorescence and thermally activated delayed fluorescence in dichloro derivatives of 9-benzoylcarbazole

Optoelectronic materials based on metal-free organic molecules represent a promising alternative to traditional inorganic devices. Significant attention has been devoted to the development of the third generation of OLEDs which are based on the temperature-activated delayed fluorescence (TADF) mechanism. In the last few years, several materials displaying ultra-long organic phosphorescence (UOP) have been designed using strategies such as crystal engineering and halogen functionalisation. Both TADF and UOP are controlled by the population of triplet states and the energy gaps between the singlet and triplet manifolds. In this paper, we explore the competition between TADF and UOP in the molecular crystals of three dichloro derivatives of 9H-carbazol-3-yl(phenyl)methanone. We investigate the excited state mechanisms in solution and the crystalline phase and address the effects of exciton transport and temperature on the rates of direct and reverse intersystem crossing under the Marcus-Levich-Jortner model. We also analyse how the presence of isomeric impurities and the stabilisation of charge transfer states affect these processes. Our simulations explain the different mechanisms observed for the three derivatives and highlight the role of intramolecular rotation and crystal packing in determining the energy gaps. This work contributes to a better understanding of the connection between chemical and crystalline structures that will enable the design of efficient materials.

Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model

We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

The LRESC-Loc Model to Analyze Magnetic Shieldings with Localized Molecular Orbitals

The leading electronic mechanisms of relativistic effects in the NMR magnetic shieldings of heavy-atom (HA) containing molecules are well described by the linear response with elimination of small components model (LRESC). We show here first results from a new version of the LRESC model written in terms of localized molecular orbitals (LMOs) which is coined as LRESC-Loc. Those LMOs resemble "chemist's orbitals", representing lone-pairs, atomic cores, and bonds. The whole set of relativistic effects are expressed in terms of non-ligand-dependent and ligand-dependent contributions. We show the electronic origin of trends and behavior of different mechanisms in molecular systems which contain heavy elements that belong to any of the IB to VIIA groups of the periodic table. The SO mechanism has a well-defined dependence with the LPs (LPσ and LPπ) when the HAs have them, but the non-SO mechanisms mostly depend on other LMOs. In addition we propose here that the SO mechanism can be used to characterize interactions involving LPs and the non-SO mechanisms to characterize covalent and close-shell interactions. All our main results are in accord with previous findings, though we are now able to analyze them in a different manner.

Redfield Propagation of Photoinduced Electron Transfer Reactions in Vacuum and Solution

Dynamical simulations of ultrafast electron transfer reactions are of utmost interest. To allow for energy dissipation directly into an external surrounding environment, a solvent coupling model has been deduced, implemented, and utilized to describe the photoinduced electron transfer dynamics within a model triad system herein. The model is based on Redfield theory, and the environment is represented by harmonic oscillators filled with bosonic quanta. To imitate real solvents, the oscillators have been equipped with frequencies and polarization lifetimes characteristic of the corresponding solvent. The population was found to transfer through the energetically lowest electron transfer route regardless of the medium. The condensed population transfer dynamics were observed to be highly dependent on the solvent parameters. In particular, an increase in the solvent coupling entailed a detainment in the population transfer from the initially prepared diabatic state and a promotion in the population transfer through the other electron transfer route. Two explanations based on the diagonal and off-diagonal matrix elements of the Kohn-Sham Fock matrix, respectively, have been provided. The lifetime of the populated partially charge-separated state was prolonged with increasing solvent polarity, and it was explained in terms of attractive interactions between the solvent's dipole moments and the fragments' charges. The high-frequency vibrational fine-structure in the correlation function was demonstrated to be important for the transfer dynamics, and the importance of dephasing effects in polar solvents was verified and precised to concern the optical polarization of the solvents.

Dissecting conjugation and electronic effects on the linear and non-linear optical properties of rhenium(I) carbonyl complexes

Herein, we report a theoretical and experimental analysis of the conjugation and electronic effects on the one-photon (1PA) and two-photon absorption (2PA) properties of a series of Re(I) carbonyl complexes with terpyridine-based ligands. An excellent agreement was obtained between the calculated and experimental 2PA spectra of the κ2N-terpyridine tricarbonyl complexes (1a-b), with 2PA cross sections reaching up to ca. 40 GM in DMF. By stepwise lowering the conjugation length in the terpy ligand and changing the local symmetry around the metal centre, we show that conjugation and delocalisation play a major role in increasing 2PA cross sections, and that the character of the excited states does not directly enhance the non-linear properties of these complexes-contrary to the results observed in 1PA. Altogether, these results give valuable guidelines towards more efficient two-photon-absorbing coordination complexes of Re(I), with potential applications in photodynamic therapy and two-photon imaging.

Photophysical Exploration of Zn(II) Polypyridine Photosensitizers in Two-Photon Photodynamic Therapy: Insights from Theory

The high incidence and difficulties of treatment of cancer have always been a challenge for mankind. Two-photon photodynamic therapy (TP-PDT) as a less invasive technique provides a new perspective for tumor treatment due to its low-energy near-infrared excitation, high targeting, and minor damage. At present, the emerging metal complexes used as the photosensitizers (PSs) in TP-PDT have aroused great interest. However, most metal complexes as PSs in TP-PDT still face some problems, such as slow clearance, unsatisfactory two-photon absorption (TPA) characteristics, high price, low reactivity, and poor solubility. In this work, density functional theory and time-dependent density functional theory were used to characterize the one/two-photon response, solvation free energy, and lipophilicity of a series of novel PSs applied in TP-PDT. The results suggest that based on complex 1, replacing Ru(II) center with Zn(II) (complex 2) can effectively prolong the triplet excited state lifetime while reducing the cost and environmental pollution, and the azetidine heterospirocycles were introduced into the ligand scaffold (complex 3), which effectively reduced the vibration relaxation of the ligand group and improved the water solubility; further, the addition of acetylenyl groups subtly enhanced the light absorption and significantly improved the two-photon response (complex 4). In addition, all complexes met the requirement of a PS and could be used as potential candidates for TP-PDT. In particular, complex 4 has the advantages of high solvation free energy, a large TPA cross-section (1413 GM), a long triplet state lifetime (671 μs), good chemical reactivity, and low cost, and it is easy to be scavenged by organisms. Overall, this contribution may provide an important clue to formulate clear design principles for type I/II PSs and rational design of PSs with high intersystem crossing rates, a long lifetime, and therapeutic excitation wavelengths.

PyMM: An Open-Source Python Program for QM/MM Simulations Based on the Perturbed Matrix Method

Quantum mechanical/molecular mechanics (QM/MM) methods are important tools in molecular modeling as they are able to couple an extended phase space sampling with an accurate description of the electronic properties of the system. Here, we describe a Python software package, called PyMM, which has been developed to apply a QM/MM approach, the perturbed matrix method, in a simple and efficient way. PyMM requires a classical atomic trajectory of the whole system and a set of unperturbed electronic properties of the ground and electronic excited states. The software output includes a set of the most common perturbed properties, such as the electronic excitation energies and the transitions dipole moments, as well as the eigenvectors describing the perturbed electronic states, which can be then used to estimate whatever electronic property. The software is composed of a simple and complete command-line interface, a set of internal input validation, and three main analyses focusing on (i) the perturbed eigenvector behavior, (ii) the calculation of the electronic absorption spectrum, and (iii) the estimation of the free energy differences along a reaction coordinate.

Site-selected thionated benzothioxanthene chromophores as heavy-atom-free small-molecule photosensitizers for photodynamic therapy

Photodynamic therapy is a clinically approved anticancer modality that employs a light-activated agent (photosensitizer) to generate cytotoxic reactive oxygen species (ROS). There is therefore a growing interest for developing innovative photosensitizing agents with enhanced phototherapeutic performances. Herein, we report on a rational design synthetic procedure that converts the ultrabright benzothioxanthene imide (BTI) dye into three heavy-atom-free thionated compounds featuring close-to-unit singlet oxygen quantum yields. In contrast to the BTI, these thionated analogs display an almost fully quenched fluorescence emission, in agreement with the formation of highly populated triplet states. Indeed, the sequential thionation on the BTI scaffold induces torsion of its skeleton reducing the singlet-triplet energy gaps and enhancing the spin-orbit coupling. These potential PSs show potent cancer-cell ablation under light irradiation while remaining non-toxic under dark condition owing to a photo-cytotoxic mechanism that we believe simultaneously involves singlet oxygen and superoxide species, which could be both characterized in vitro. Our study demonstrates that this simple site-selected thionated platform is an effective strategy to convert conventional carbonyl-containing fluorophores into phototherapeutic agents for anticancer PDT.

Accurate Prediction of Vertical Ionization Potentials and Electron Affinities from Spin-Component Scaled CC2 and ADC(2) Models

The CC2 and ADC(2) wave function models and their spin-component scaled modifications are adopted for predicting vertical ionization potentials (VIPs) and electron affinities (VEAs). The ionic solutions are obtained as electronic excitations in the continuum orbital formalism, making possible the use of existing, widespread quantum chemistry codes with minimal modifications, in full consistency with the treatment of charge transfer excitations. The performance of different variants is evaluated via benchmark calculations on various sets from previous works, containing small- and medium-sized systems, including the nucleobases. It is shown that with the spin-scaled approximate methods, in particular the scaled opposite-spin variant of the ADC(2) method, the accuracy of EOM-CCSD is achievable at a fraction of the computational cost, also outperforming many common electron propagator approaches.

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.

Persistent and Efficient Multimodal Imaging for Tyrosinase Based on Two-Photon Excited Fluorescent and Room-Temperature Phosphorescent Probes

Tyrosinase is crucial to regulate the metabolism of phenol derivatives, playing an important role in the biosynthesis of melanin pigments, whereas an abnormal level of tyrosinase would lead to severe diseases. It is rather necessary to develop a sensitive and selective imaging tool to assess the level of tyrosinase in vivo. We thoroughly researched the luminous mechanism of the existing TPTYR probe and provided design strategies to improve its two-photon excited fluorescence properties. The designed probes benza2-TPTYR and product benza2-TPTYR-coumarin have large two-photon absorption cross sections at the NIR spectral region (41 GM/706 nm, 71 GM/852 nm), while benza2-TPTYR-coumarin possesses easily distinguishable spectrum in the visible region and a high fluorescence efficiency (Φ_F = 0.27). What is more, novel two-photon excited multimodal imaging based on the pure organic small molecule benza1-TPTYR-coumarin (61 GM/936 nm) is proposed first, simultaneously possessing strong instantaneous fluorescent (563.79 nm) and persistent room-temperature phosphorescent emissions (767.68 nm, 0.54 ms).

Modulating the Chiroptical Response of Chiral Polymers with Extended Conjugation within the Structural Building Blocks

Advancing the emerging area of chiral photonics requires modeling-guided concepts of chiral material design to enhance optical activity and associated optical rotatory dispersion. Herein, we introduce conformational engineering achieved by tuning polymer backbone conjugation through introduction of thiophene structural units in a chiral fluorene polymer backbone. Our theoretical calculations reveal a relationship between the structural conformation and the resultant rotational strength. We further synthesize a series of chiral fluorene-based polymers copolymerized with thiophene whose optical chirality trend is in qualitative agreement with predictions of our quantum chemical calculations. Varying the number of thiophene units in the monomer building block allows us to modulate the rotational strength by tuning the intrafibril helicity of single-stranded polymer chains, whereby the monomer conjugation is retained throughout the whole length of the polymer backbone. Our design concept delineates an underexamined approach: the concept of tuning backbone conjugation and helicity within the main chain to enhance the optical activity of chiral polymer systems.

High efficient room temperature phosphorescent materials constructed with methylene molecular configuration

In this work, we have investigated several pure organic room temperature phosphorescent materials with donor-methylene acceptor configurations with relatively different quantum efficiency. The results show that the introduction of methylene functional group in room temperature phosphorescent materials based on donor-acceptor configuration is more favorable for obtaining higher phosphorescent quantum efficiency in crystal phase environment. More importantly, our calculations reveal the root cause of the excellent quantum efficiency performance after the introduction of methylene groups. The results show that the introduction of methylene can inhibit the structural deformation of molecules during the excited state transition process and give them higher interaction. Moreover, in the donor-acceptor configuration, the heavy atom effect is more favorable to the formation of π-x (X = Br) interaction to accelerate the occurrence of intersystem crossing and achieve a higher intersystem crossing rate. Therefore, the donor-methylene-acceptor molecule is expected to improve the quantum efficiency of room temperature phosphorescence, and the addition of heavy atoms is more conducive to prolong the life of room temperature phosphorescence. This work provides a useful reference for rational design of room temperature phosphorescent materials with high efficiency and long life.

A new framework for frequency-dependent polarizable force fields

A frequency-dependent extension of the polarizable force field "Atom-Condensed Kohn-Sham density functional theory approximated to the second-order" (ACKS2) [Verstraelen et al., J. Chem. Phys. 141, 194114 (2014)] is proposed, referred to as ACKS2ω. The method enables theoretical predictions of dynamical response properties of finite systems after partitioning of the frequency-dependent molecular response function. Parameters in this model are computed simply as expectation values of an electronic wavefunction, and the hardness matrix is entirely reused from ACKS2 as an adiabatic approximation is used. A numerical validation shows that accurate models can already be obtained with atomic monopoles and dipoles. Absorption spectra of 42 organic and inorganic molecular monomers are evaluated using ACKS2ω, and our results agree well with the time-dependent DFT calculations. Also for the calculation of C₆ dispersion coefficients, ACKS2ω closely reproduces its TDDFT reference. When parameters for ACKS2ω are derived from a PBE/aug-cc-pVDZ ground state, it reproduces experimental values for 903 organic and inorganic intermolecular pairs with an MAPE of 3.84%. Our results confirm that ACKS2ω offers a solid connection between the quantum-mechanical description of frequency-dependent response and computationally efficient force-field models.