Interpretation of molecular electron transport in ab initio many-electron framework incorporating zero-point nuclear motion effects.

A computational methodology, founded on chemical concepts, is presented for interpreting the role of nuclear motion in the electron transport through single-molecule junctions (SMJ) using many-electron ab initio quantum chemical calculations. Within this approach the many-electron states of the system, computed at the SOS-ADC(2) level, are followed along the individual normal modes of the encapsulated molecules. The inspection of the changes in the partial charge distribution of the many-electron states allows the quantification of the electron transport and the estimation of transmission probabilities. This analysis improves the understanding of the relationship between internal motions and electron transport. Two SMJ model systems are studied for validation purposes, constructed from a conductor (BDA, benzene-1,4-diamine) and an insulator molecule (DABCO, 1,4-diazabicyclo[2.2.2]octane). The trends of the resulting transmission probabilities are in agreement with the experimental observations, demonstrating the capability of the approach to distinguish between conductor and insulator type systems, thereby offering a straightforward and cost-effective tool for such classifications via quantum chemical calculations.

Projected Atomic Orbitals As Optimal Virtual Space for Excited State Projection-Based Embedding Calculations.

The projected atomic orbital (PAO) technique is presented for the construction of virtual orbital spaces in projection-based embedding (PbE) applications. The proposed straightforward procedure produces a set of virtual orbitals that are used in the final, high-level calculation of the embedded active subsystem. The PAO scheme is demonstrated on intermolecular potentials of bimolecular complexes in ground and excited states, including Rydberg excitations. The results show the outstanding performance of the PbE method when used with PAO virtual orbitals compared with those produced using common orbital localization techniques. The good agreement of the resulting PbE potential curves with those from high-level ab initio dimer calculations, also in diffuse basis sets, confirms that the PAO technique can be suggested for future applications using top-down embedding methods.

Ab initio investigation of excited state charge transfer pathways in differently capped bithiophene cages.

The electronic excitations of conformationally constrained bithiophene cage systems as previously investigated by Lewis et al. (J. Am. Chem. Soc. 143, 18548 (2021)) are revisited, employing the correlated ab initio Scaled Opposite-Spin Algebraic Diagrammatic Construction Second Order electronic structure method. Quantitative descriptors are determined to assess the extent of charge transfer between the bithiophene moieties and the capping domains, represented by either phenyl or triazine groups. The investigation substantiates intrinsic differences in the photophysical behavior of these two structural variants and reveals the presence of lower-energy excited states characterized by noteworthy charge transfer contributions in the triazine cage system. The manifestation of this charge transfer character is discernible even at the Franck-Condon geometry, persisting throughout the relaxation of the excited state. By examining isolated monomer building blocks, we confirm the existence of analogous charge transfer contributions in their excitations. Employing this methodological approach facilitates the prospective identification of potential wall/cap chromophore pairs, wherein charge transfer pathways can be accessed within the energetically favorable regime.

Benchmarking Aspects of Ab Initio Fragment Models for Accurate Excimer Potential Energy Surfaces.

While Coupled-Cluster methods have been proven to provide an accurate description of excited electronic states, the scaling of the computational costs with the system size limits the degree for which these methods can be applied. In this work different aspects of fragment-based approaches are studied on noncovalently bound molecular complexes with interacting chromophores of the fragments, such as π-stacked nucleobases. The interaction of the fragments is considered at two distinct steps. First, the states localized on the fragments are described in the presence of the other fragment(s); for this we test two approaches. One method is founded on QM/MM principles, only including the electrostatic interaction between the fragments in the electronic structure calculation with Pauli repulsion and dispersion effects added separately. The other model, a Projection-based Embedding (PbE) using the Huzinaga equation, includes both electrostatic and Pauli repulsion and only needs to be augmented by dispersion interactions. In both schemes the extended Effective Fragment Potential (EFP2) method of Gordon et al. was found to provide an adequate correction for the missing terms. In the second step, the interaction of the localized chromophores is modeled for a proper description of the excitonic coupling. Here the inclusion of purely electrostatic contributions appears to be sufficient: it is found that the Coulomb part of the coupling provides accurate splitting of the energies of interacting chromophores that are separated by more than 4 Å.

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.

Performance of Multilevel Methods for Excited States.

The performance of multilevel quantum chemical approaches, which utilize an atom-based system partitioning scheme to model various electronic excited states, is studied. The considered techniques include the mechanical-embedding (ME) of "our own N-layered integrated molecular orbital and molecular mechanics" (ONIOM) method, the point charge embedding (PCE), the electronic-embedding (EE) of ONIOM, the frozen density-embedding (FDE), the projector-based embedding (PbE), and our local domain-based correlation method. For the investigated multilevel approaches, the second-order algebraic-diagrammatic construction [ADC(2)] approach was utilized as the high-level method, which was embedded in either Hartree-Fock or a density functional environment. The XH-27 test set of Zech et al. [ J. Chem. Theory Comput., 2018, 14, 4028] was used for the assessment, where organic dyes interact with several solvent molecules. With the selection of the chromophores as active subsystems, we conclude that the most reliable approach is local domain-based ADC(2) [L-ADC(2)], and the least robust schemes are ONIOM-ME and ONIOM-EE. The PbE, FDE, and PCE techniques often approach the accuracy of the L-ADC(2) scheme, but their precision is far behind. The results suggest that a more conservative subsystem selection algorithm or the inclusion of subsystem charge-transfers is required for the atom-based cost-efficient methods to produce high-accuracy excitation energies.

Comparison of approximate intermolecular potentials for ab initio fragment calculations on medium sized N-heterocycles.

The ground state intermolecular potential of bimolecular complexes of N-heterocycles is analyzed for the impact of individual terms in the interaction energy as provided by various, conceptually different theories. Novel combinations with several formulations of the electrostatic, Pauli repulsion, and dispersion contributions are tested at both short- and long-distance sides of the potential energy surface, for various alignments of the pyrrole dimer as well as the cytosine-uracil complex. The integration of a DFT/CCSD density embedding scheme, with dispersion terms from the effective fragment potential (EFP) method is found to provide good agreement with a reference CCSD(T) potential overall; simultaneously, a quantum mechanics/molecular mechanics approach using CHELPG atomic point charges for the electrostatic interaction, augmented by EFP dispersion and Pauli repulsion, comes also close to the reference result. Both schemes have the advantage of not relying on predefined force fields; rather, the interaction parameters can be determined for the system under study, thus being excellent candidates for ab initio modeling.

Improved Description of Charge-Transfer Potential Energy Surfaces via Spin-Component-Scaled CC2 and ADC(2) Methods.

The molecular level understanding of electronic transport properties depends on the reliable theoretical description of charge-transfer (CT)-type electronic states. In this paper, the performance of spin-component-scaled variants of the popular CC2 and ADC(2) methods is evaluated for CT states, following benchmark strategies of earlier studies that revealed a compromised accuracy of the unmodified models. In addition to statistics on the accuracy of vertical excitation energies at equilibrium and infinite separation of bimolecular complexes, potential energy surfaces of the ammonia-fluorine complex are also reported. The results show the capability of spin-component-scaled approaches to reduce the large errors of their regular counterparts to a significant extent, outperforming even the coupled-cluster single and double method in many cases. The cost-effective scaled-opposite-spin variants are found to provide a remarkably good agreement with the CCSDT-3 reference data, thereby being recommended methods of choice in the study of charge-transfer states.

Diagonal Born-Oppenheimer corrections to the ground electronic state potential energy surfaces of ozone: improvement of ab initio vibrational band centers for the 16O3, 17O3 and 18O3 isotopologues.

Mass-dependent diagonal Born-Oppenheimer corrections (DBOCs) to the ab initio electronic ground state potential energy surface for the main 16O3 isotopologue and for homogeneous isotopic substitutions 17O3 and 18O3 of the ozone molecule are reported for the first time. The system being of strongly multiconfigurational character, multireference configuration interaction wave function ansatz with different complete active spaces was used. The reliable DBOC calculations with the targeted accuracy were possible to carry out up to about half of the dissociation threshold D0. The comparison with the experimental band centers shows a significant improvement of the accuracy with respect to the best Born-Oppenheimer (BO) ab initio calculations reducing the total root-mean-squares (calculated-observed) deviations by about a factor of two. For the set of 16O3 vibrations up to five bending and four stretching quanta, the mean (calculated-observed) deviations drop down from 0.7 cm-1 (BO) to about 0.1 cm-1, with the most pronounced improvement seen for bending states and for mixed bending-stretching polyads. In the case of bending band centers directly observed under high spectral resolutions, the errors are reduced by more than an order of magnitude down to 0.02 cm-1 from the observed levels, approaching nearly experimental accuracy. A similar improvement for heavy isotopologues shows that the reported DBOC corrections almost remove the systematic BO errors in vibrational levels below D0/2, though the scatter increases towards higher energies. The possible reasons for this finding, as well as remaining issues are discussed in detail. The reported results provide an encouraging accuracy validation for the multireference methods of the ab initio theory. New sets of ab initio vibrational states can be used for improving effective spectroscopic models for analyses of the observed high-resolution spectra, particularly in the cases of accidental resonances with "dark" states requiring accurate theoretical predictions.

A New Benchmark Set for Excitation Energy of Charge Transfer States: Systematic Investigation of Coupled Cluster Type Methods.

The numerous existing publications on benchmarking quantum chemistry methods for excited states rarely include Charge Transfer (CT) states, although many interesting phenomena in, e.g., biochemistry and material physics involve the transfer of electrons between fragments of the system. Therefore, it is timely to test the accuracy of quantum chemical methods for CT states, as well. In this study we first propose a new benchmark set consisting of dimers having low-energy CT states. On this set, the vertical excitation energy has been calculated with Coupled Cluster methods including triple excitations (CC3, CCSDT-3, CCSD(T)(a)*), as well as with methods including full or approximate doubles (CCSD, STEOM-CCSD, CC2, ADC(2), EOM-CCSD(2)). The results show that the popular CC2 and ADC(2) methods are much less accurate for CT states than for valence states. On the other hand, EOM-CCSD seems to have similar systematic overestimation of the excitation energies for both types of states. Among the triples methods the novel EOM-CCSD(T)(a)* method including noniterative triple excitations is found to stand out with its consistently good performance for all types of states, delivering essentially EOM-CCSDT quality results.

Coupled-cluster techniques for computational chemistry: The CFOUR program package.

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry.

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Accuracy of Spin-Component Scaled ADC(2) Excitation Energies and Potential Energy Surfaces.

In a recent paper of this journal ( Tajti ; ; Szalay . J. Chem. Theory Comput. 2019 , 15 , 5523 ), we have shown that failures of the CC2 method to describe Rydberg excited states as well as potential energy surfaces of certain valence excited states can be cured by spin-component scaled (SCS) versions SCS-CC2 and SOS-CC2 to a large extent. In this paper, the related and popular second-order algebraic diagrammatic construction (ADC(2)) method and its SCS variants are inspected with the previously established methodology. The results reflect the similarity of the CC2 and ADC(2) models, showing identical problems in the case of the canonical form and the same improvement when spin-component scaling is applied.

Accuracy of Spin-Component-Scaled CC2 Excitation Energies and Potential Energy Surfaces.

Benchmark calculations with the Spin-Component-Scaled CC2 variants SCS-CC2 and SOS-CC2 are presented for the electronically excited valence and Rydberg states of small- and medium-sized molecules. Besides the vertical excitation energies and excited state gradients, the potential energy surfaces are also investigated via scans following the forces that act in the Franck-Condon region. The results are compared to the regular CC2 ones, as well as higher level methods CCSD, CCSD(T)(a)*, and CCSDT. The results indicate that a large fraction of the flaws of CC2 revealed by earlier studies disappears if spin-component scaling is employed. This makes these variants attractive alternatives of their unscaled counterparts, offering competitive accuracy of vertical excitation energies of both valence and Rydberg type states and reliable potential energy surfaces, while also maintaining a low-power-scaling computational cost with the system size.

Accuracy of Coupled Cluster Excited State Potential Energy Surfaces.

The validation of the quality of the description of excited electronic states is of special importance in quantum chemistry as the general reliability of ab initio methods shows a much larger variation for these states than for the ground state. In this study, we investigate the quality of excited state energy gradients and potential energy surfaces on selected systems, as provided by the single reference coupled cluster variants CC2, CCSD, CCSD(T)(a)*, and CC3. Gradients and surface plots that follow the Franck-Condon forces are compared to the respective CCSDT reference values, thereby establishing a useful strategy for judging each variant's accuracy. The results reveal serious flaws of lower order methods - in particular, CC2 - in several situations where they otherwise give accurate vertical excitation energies, as well as excellent accuracy and consistency of the recently proposed CCSD(T)(a)* method.

Multireference Approaches for Excited States of Molecules.

Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications.

Dimol Emission of Oxygen Made Possible by Repulsive Interaction.

For the energy emitted in a textbook example of chemiluminescence, the peculiar red light produced by singlet molecular oxygen is about twice that of the spin-forbidden O2(a1Δg) → O2(X3∑g-) transition. Theoretical studies suggest that the O2(a1Δg)-O2(a1Δg) van der Waals interaction is weak, and at room temperature no long-lived complex is formed. Our high-level ab initio calculations show that in the bound domain of the dimer, the oscillator strength is very small, but increases at smaller intermolecular separations, where, however, the interaction is repulsive. We propose that the emission is induced by collisions: it takes place "on-the-fly", when the collision energy allows the system to access the repulsive part of the potential energy surface where the oscillator strength is relatively large. The contribution of different orientations of the two O2 molecules to the emission has been evaluated with a simple semiclassical model. The position of the emission peak is in accord with the experiment, and the estimated rate coefficient of collision-induced emission averaged over orientation is in reasonable agreement with the measurements.

Fourier Transform Microwave Spectrum of Propene-3-d1 (CH2═CHCH2D), Quadrupole Coupling Constants of Deuterium, and a Semiexperimental Equilibrium Structure of Propene.

The ground-state rotational spectrum of propene-3-d1, CH2═CHCH2D, was measured by Fourier transform microwave spectroscopy. Transitions were assigned for the two conformers, one with the D atom in the symmetry plane (S) and the other with the D atom out of the plane (A). The energy difference between the two conformers was calculated to be 6.5 cm-1, the S conformer having lower energy. The quadrupole hyperfine structure due to deuterium was resolved and analyzed for both conformers. The experimental quadrupole coupling and the centrifugal distortion constants compared favorably to their ab initio counterparts. Ground-state rotational constants for the S conformer are 40582.157(9), 9067.024(1), and 7766.0165(12) MHz. Ground-state rotational constants for the A conformer are 43403.75(3), 8658.961(2), and 7718.247(2) MHz. For the A conformer, a small tunneling splitting (19 MHz) due to internal rotation was observed and analyzed. Using the new rotational constants of this work as well as those previously determined for the 13C species and for some deuterium-substituted species from the literature, a new semiexperimental equilibrium structure was determined and its high accuracy was confirmed. The difficulty in obtaining accurate coordinates for the out-of-plane hydrogen atom is discussed.

Accuracy of Coupled Cluster Excitation Energies in Diffuse Basis Sets.

We present a comprehensive statistical analysis on the accuracy of various excited state Coupled Cluster methods, accentuating the effect of diffuse basis sets on vertical excitation energies of valence and Rydberg-type states. Many popular approximate doubles and triples methods are benchmarked with basis sets up to aug-cc-pVTZ, with high level EOM-CCSDT results used as reference. The results reveal a serious deficiency of CC2 linear response and CIS(D) techniques in the description of Rydberg states, a feature not shown by the EOM-CCSD(2) and EOM-CCSD variants. The CC3 theory proves to be an accurate choice among the iterative approximate triples methods, while the novel perturbation-based CCSD(T)(a)* variant turns out to be the best way to include the effect of triple excitations in a noniterative way.

Investigation of the Impact of Different Terms in the Second Order Hamiltonian on Excitation Energies of Valence and Rydberg States.

Describing electronically excited states of molecules accurately poses a challenging problem for theoretical methods. Popular second order techniques like Linear Response CC2 (CC2-LR), Partitioned Equation-of-Motion MBPT(2) (P-EOM-MBPT(2)), or Equation-of-Motion CCSD(2) (EOM-CCSD(2)) often produce results that are controversial and are ill-balanced with their accuracy on valence and Rydberg type states. In this study, we connect the theory of these methods and, to investigate the origin of their different behavior, establish a series of intermediate variants. The accuracy of these on excitation energies of singlet valence and Rydberg electronic states is benchmarked on a large sample against high-accuracy Linear Response CC3 references. The results reveal the role of individual terms of the second order similarity transformed Hamiltonian, and the reason for the bad performance of CC2-LR in the description of Rydberg states. We also clarify the importance of the T̂1 transformation employed in the CC2 procedure, which is found to be very small for vertical excitation energies.