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.

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.

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.

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.

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.

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.

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.

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.

Characterization of the excited states of DNA building blocks: a coupled cluster computational study.

DNA building blocks consisting of up to four nucleobases are investigated using the EOM-CCSD and CC2-LR methods in two B-DNA-like arrangements of a poly-adenine:poly-thymine (poly-A:poly-T) system. Excitation energies and oscillator strengths are presented and the characteristics of the excited states are discussed. Excited states of single-stranded poly-A systems are highly delocalized, especially the spectroscopically bright states, where delocalization over up to four fragments can be observed. In the case of poly-T systems, the states are somewhat less delocalized, extending to maximally about three fragments. A single A:T Watson-Crick pair has highly localized states, while delocalization over base pairs can be observed for some excited states of the (A)2:(T)2 system, but intrastrand delocalization is more pronounced in this case, as well. As for the characteristics of the simulated UV absorption spectra, a significant decrease of intensity can be observed in the case of single strands with increasing chain length; this is due to the stacking interactions and is in accordance with previous results. On the other hand, the breaking of H-bonds between the two strands does not alter the spectral intensity considerably, it only causes a redshift of the absorption band, thus it is unable to explain the experimentally observed DNA hyperchromism on its own, and stacking interactions need to be considered for the description of this effect as well.

Quantum chemical MP2 results on some hydrates of cytosine: binding sites, energies and the first hydration shell.

A detailed quantum chemical investigation was undertaken to obtain the structure and energetics of cytosine hydrates Cyt·nH2O, with n = 1 to 7. The MP2(fc)/aug-cc-pVDZ level was used as the standard, with some DFT (B3LYP) and coupled cluster calculations, as well as calculations with the aug-cc-pVTZ basis set added for comparison. In a systematic search for microhydrated forms of cytosine, we have found that several structures have not yet been reported in the literature. The energies of different isomers, as well as binding energies are compared. When predicting the stability of a complex, we suggest using a scheme where the water molecules are extracted from a finite model of bulk water. Finally, based on energetic data, we suggest a rational definition of the first hydration shell; with this definition, it contains just six water molecules.

Development of highly accurate approximate scheme for computing the charge transfer integral.

The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the "exact" scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the "exact" calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.

Code interoperability and standard data formats in quantum chemistry and quantum dynamics: The Q5/D5Cost data model.

Code interoperability and the search for domain-specific standard data formats represent critical issues in many areas of computational science. The advent of novel computing infrastructures such as computational grids and clouds make these issues even more urgent. The design and implementation of a common data format for quantum chemistry (QC) and quantum dynamics (QD) computer programs is discussed with reference to the research performed in the course of two Collaboration in Science and Technology Actions. The specific data models adopted, Q5Cost and D5Cost, are shown to work for a number of interoperating codes, regardless of the type and amount of information (small or large datasets) to be exchanged. The codes are either interfaced directly, or transfer data by means of wrappers; both types of data exchange are supported by the Q5/D5Cost library. Further, the exchange of data between QC and QD codes is addressed. As a proof of concept, the H + H2 reaction is discussed. The proposed scheme is shown to provide an excellent basis for cooperative code development, even across domain boundaries. Moreover, the scheme presented is found to be useful also as a production tool in the grid distributed computing environment.

Details of the excited-state potential energy surfaces of adenine by coupled cluster techniques.

EOM-CCSD and CC2-LR methods were used to study the potential energy surfaces of the three lowest excited states (two ππ* and an nπ*) of adenine. The equilibrium structure could only be obtained for the S1 state, which has n-π* character. It was shown that the topology of the coupled cluster surface is such that no minimum for the S2 and S3 states exists in the Franck-Condon region due to conical intersections between these low-lying states. To understand this topology, relevant cuts of the potential energy surfaces have also been calculated, and conical intersections have been located. Even a three-fold intersection between these three states was found. The crossings of these surfaces can be reached from the bright state barrierlessly without major change in the geometry. Therefore, these might play an important role in the ultrafast deactivation of adenine.

A new accurate ground-state potential energy surface of ethylene and predictions for rotational and vibrational energy levels.

In this paper we report a new ground state potential energy surface for ethylene (ethene) C2H4 obtained from extended ab initio calculations. The coupled-cluster approach with the perturbative inclusion of the connected triple excitations CCSD(T) and correlation consistent polarized valence basis set cc-pVQZ was employed for computations of electronic ground state energies. The fit of the surface included 82,542 nuclear configurations using sixth order expansion in curvilinear symmetry-adapted coordinates involving 2236 parameters. A good convergence for variationally computed vibrational levels of the C2H4 molecule was obtained with a RMS(Obs.-Calc.) deviation of 2.7 cm(-1) for fundamental bands centers and 5.9 cm(-1) for vibrational bands up to 7800 cm(-1). Large scale vibrational and rotational calculations for (12)C2H4, (13)C2H4, and (12)C2D4 isotopologues were performed using this new surface. Energy levels for J = 20 up to 6000 cm(-1) are in a good agreement with observations. This represents a considerable improvement with respect to available global predictions of vibrational levels of (13)C2H4 and (12)C2D4 and rovibrational levels of (12)C2H4.

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.

Benchmark studies on the building blocks of DNA. 3. Watson-Crick and stacked base pairs.

Excited states of stacked adenine-thymine and guanine-cytosine pairs as well as the Watson-Crick pair of guanine-thymine have been investigated using the equation of motion coupled-cluster (EOM-CC) method with single and double as well as approximate triple excitations. Transitions have been assigned, and the form of the excitations has been analyzed. The majority of the excitations could be classified as localized on the nucleobases, but for all three studied systems, charge-transfer (CT) transitions could also be identified. The main aim of this study was to compare the performance of lower-level methods (ADC(2) and TDDFT) to the high-level EOM-CC ones. It was shown that both ADC(2) and TDDFT with long-range correction have nonsystematic error in excitation energies, causing alternation of the energetic ordering of the excitations. Considering the high costs of the EOM-CC calculations, there is a need for reliable new approximate methods.

Benchmarking for perturbative triple-excitations in EE-EOM-CC methods.

Perturbative triples corrections ((T) and (T̃)) to the equation of motion coupled cluster singles and doubles (EOM-CCSD) are rederived and implemented in a pilot parallel code. The vertical excitation energies of molecules in the test set of Sauer et al. [J. Chem. Theor. Comput. 2009, 5, 555] are reported and compared to the iterative EOM-CCSDT-3 method. The average absolute deviations of EOM-CCSD(T) and EOM-CCSD(T̃) from EOM-CCSDT-3 over this wide test set are 0.06 and 0.18 eV, respectively. The poor performance of the latter suggests misbalanced handling of the (T̃) terms. Scaling curves for EOM-CCSD(T) are also presented to demonstrate the performance across multiple compute nodes, thus enabling the routine and accurate study of excited states for ever larger molecular systems.

New analytical model for the ozone electronic ground state potential surface and accurate ab initio vibrational predictions at high energy range.

An accurate description of the complicated shape of the potential energy surface (PES) and that of the highly excited vibration states is of crucial importance for various unsolved issues in the spectroscopy and dynamics of ozone and remains a challenge for the theory. In this work a new analytical representation is proposed for the PES of the ground electronic state of the ozone molecule in the range covering the main potential well and the transition state towards the dissociation. This model accounts for particular features specific to the ozone PES for large variations of nuclear displacements along the minimum energy path. The impact of the shape of the PES near the transition state (existence of the "reef structure") on vibration energy levels was studied for the first time. The major purpose of this work was to provide accurate theoretical predictions for ozone vibrational band centres at the energy range near the dissociation threshold, which would be helpful for understanding the very complicated high-resolution spectra and its analyses currently in progress. Extended ab initio electronic structure calculations were carried out enabling the determination of the parameters of a minimum energy path PES model resulting in a new set of theoretical vibrational levels of ozone. A comparison with recent high-resolution spectroscopic data on the vibrational levels gives the root-mean-square deviations below 1 cm(-1) for ozone band centres up to 90% of the dissociation energy. New ab initio vibrational predictions represent a significant improvement with respect to all previously available calculations.

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.