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Resonance via Pade (RVP) is an efficient method for calculating autoionization resonance states. It is based on the stabilization technique in which the basis set is scaled. The scaling can be uniform (i.e., all basis functions are scaled) or partial. Herein, we compare the two RVP scaling schemes for calculating an autoionization eigenvalue; moreover, the effect of freezing the core electrons is intertwined within this comparison. In order to study the different behavior of the RVP schemes, we associate each RVP scaling scheme with a complex contour of integration. Similarities between RVP and other non-Hermitian methods emerge from the generated contours, which suggest that RVP introduces similar outgoing boundary conditions as the complex scaling (CS), complex basis function (CBF), and reflection-free complex absorbing potential (RF-CAP) methods. A uniform-RVP contour, unlike a partial one, immediately penetrates the complex plane and influences the interaction region. Hence, uniform scaling within RVP destroys the description of the core electrons, as well as the description of the reference state, and yields less reliable results than partial scaling. The 1s22p3s1P autoionization state of Be, at the equation-of-motion coupled-cluster level, is used as our case study model.

Electronic transition dipoles are crucial for investigating light-matter interactions. Transition dipoles between metastable (autoionizing resonance) states become complex within non-Hermitian formalism, analogous to the resonance energies. Herein, we put forward a robust method for evaluating complex transition dipoles based on real ab initio stabilization calculations. The complex transition dipoles are obtained by analytical continuation via the Pade approximant and are identified as stationary solutions in the complex plane. The capability of the new approach is demonstrated for several transition dipoles of the doubly excited helium resonance states, for which exact values are available for comparison. Nevertheless, the method presented here has no inherent limitation and is suitable for polyatomic systems.

Noble-gas spins feature hours long coherence times owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically-excited potassium atoms and reveal the formation of quasi-bound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to six orders of magnitude and two orders of magnitude enhancement for the thermally averaged, polarization rate-coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized., 8 pages, 4 figures in the main text, appended to the end are 12 pages, 4 figures of supplementary information

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design. This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Atomic and molecular resonances play an important role in many physical processes, hence developing theoretical tools to properly calculate these states is required. Recently, we introduced a method for calculating the electronic resonance complex energies from stabilization graphs via analytical continuation, specifically, using the Padé approximant. This method was shown to be efficient, for example, in interpreting the results of cold molecular collisions. However, we observed that the complex energies obtained by Padé depend on the selected set of input points from the stabilization graph. In addition, unphysical solutions (noise) may appear and need to be eliminated. Therefore, applying the method to systems in which the resonance values are unavailable is difficult. The excited Li-He* Feshbach states, for which autoionization was recently observed, present such a challenge. Herein, we introduce a statistical approach to single out the resonance energy from the false solutions by identifying it as a cluster of Padé solutions. This clusterization technique was applied to study several electronic resonance states, for which we obtained excellent agreement with available data (exact or other theoretical solutions and an experimental result). Following this, the technique successfully identified the most likely Li-He* Feshbach resonance energy. Moreover, we concluded that large input sets generate much noise while restricting the number of points facilitates clusterization, which makes this approach more attractive, since input points are obtained from computationally demanding electronic-structure calculations. Overall, the use of analytical continuation via Padé, along with the statistical technique presented herein, offers an efficient approach to calculate resonances.

Resonance via Padé (RVP) is an efficient method for calculating autoionization resonance states. It is based on the stabilization technique in which the basis set is scaled. The scaling can be uniform (i.e., all basis functions are scaled) or partial. Herein, we compare the two RVP scaling schemes for calculating an autoionization eigenvalue; moreover, the effect of freezing the core electrons is intertwined within this comparison. In order to study the different behavior of the RVP schemes, we associate each RVP scaling scheme with a complex contour of integration. Similarities between RVP and other non-Hermitian methods emerge from the generated contours, which suggest that RVP introduces similar outgoing boundary conditions as the complex scaling (CS), complex basis function (CBF), and reflection-free complex absorbing potential (RF-CAP) methods. A uniform-RVP contour, unlike a partial one, immediately penetrates the complex plane and influences the interaction region. Hence, uniform scaling within RVP destroys the description of the core electrons, as well as the description of the reference state, and yields less reliable results than partial scaling. The 1

Stabilisation technique is a traditional approach for studying resonances, such as the metastable autoionisation states. Stabilisation graphs are usually calculated by scaling the employed basis functions. Over the years, many methods for extracting the resonance complex energies from these graphs have been developed, nowadays, they are usually evaluated via analytical continuation schemes. However, many times it is difficult to obtain a well-behaved stabilisation graphs upon basis-set scaling. Herein, we illustrate that it is possible to shape stabilisation graphs to behave physically by adjusting the relevant Gaussian basis function exponents. We illustrate this for the excited Li–He∗ 2Σ and 2Π states [with He∗(1s2p; 1P)], which serve as an excellent example since generating well-behaved graphs in this case is challenging. We show that by controlling and shaping the stabilisation graphs we can obtain converged complex energies, which are calculated by the resonances via Pade approach (a recently...

The quantum phenomena of electronic and nuclear resonances are associated with structures in measured cross sections. Such structures were recently reported in a cold chemistry experiment of ground-state hydrogen isotopologues (H2/HD) colliding with helium atoms in the excited triplet P-state (He(23P)) [Shagam et al. Nature Chem. 2015, 7, 921], but a theoretical explanation of their appearance was not given. This work presents a quantum explanation and simulation of this experiment, which are strictly based on ab initio calculations. We incorporate complex potential energy surfaces into adiabatic variational theory, thereby reducing the multidimensional scattering process to a series of uncoupled 1D scattering “gedanken experiments”. Our theoretical result, which is in remarkable agreement with the experimental data, manifests that the structures in the observed reaction rate coefficient are due to the spatial arrangement of the excited He p-orbitals with respect to the interaction axis, consequently chan...

LiHe is an intriguing open-shell dimer. It is an extremely weakly bound system, and its vibrational bound-state radius extends far into the classically forbidden regions. Exciting helium into 1s2p leads to a

Absorption of slow moving electrons by neutral ground state nucleobases has been known to produce resonance metastable states. There are indications that such metastable states may play a key role in DNA/RNA damage. Therefore, herein, we present an ab initio non-Hermitian investigation of the resonance positions and decay rates for the low lying shape-type states of the uracil anion. In addition, we calculate the complex transition dipoles between these resonance states. We employ the resonance via Padé (RVP) method to calculate these complex properties from real stabilization curves by analytical dilation into the complex plane. This method has already been successfully applied to many small molecular systems, and herein, we present the first application of RVP to a medium-sized system. The presented resonance energies are optimized with respect to the size of the basis set and compared with previous theoretical studies and experimental findings. Complex transition dipoles between the shape-type resonances are computed using the optimal basis set. The ability to calculate ab initio energies and lifetimes of biologically relevant systems paves the way for studying reactions of such systems in which autoionization takes place, while the ability to also calculate their complex transition dipoles opens the door for studying photo-induced dynamics of such biological molecules.

LiHe is an extreme open-shell system. It is among the weakest bound systems known, and its mean interatomic distance extends dramatically into the classical forbidden region. Upon 1s → 2p excitation of He, interatomic Coulombic decay (ICD) takes place in which the electronically excited helium atom relaxes and transfers its excess energy to ionize the neighboring lithium atom. A substantial part of the decay is found to be to the dissociation continuum producing Li

LiHe is an intriguing open-shell dimer. It is an extremely weakly bound system, and its vibrational bound-state radius extends far into the classically forbidden regions. Exciting helium into 1s2p leads to a 2Σ and a 2Π state, in which lithium is in its ground state. These states are located above the ionization threshold of the Li atom, which makes them metastable, i.e., resonance states. Under these conditions, energy transfer between the atoms over large distances is feasible within the framework of interatomic Coulombic decay (ICD). These states are investigated theoretically; herein, we present and analyze the complex potential energy curves of the 2Σ and 2Π states, where their imaginary parts describe the decay rate of these resonance states. We employ the resonance via Pade approach to calculate these potentials. Thereby, we use the equation-of-motion coupled-cluster method to compute stabilization graphs as input data for the analytical dilation (via Pade) into the complex energy plane. The procedure is suitable for studying Feshbach resonances and ICD states such as the LiHe 2Σ and 2Π states. The resulting ab initio complex potential energy curves will be used in future work to describe the dynamics of the process HeLi + hν → He*Li → HeLi+ + eICD, which is amenable to experiment.

An accurate description of both bound and resonance states is desirable in the study of molecules. However, it is not a trivial task to accomplish, as theoretical and numerical formalisms developed for describing one do not always fit for describing the other. One such formalism, mainly designed to describe resonances, is the complex scaling method, in which the Hamiltonian internal coordinates are scaled by a complex factor of eiθ. As Kapralova-Žďanska and Smydke recently showed in their study on helium, in order to well describe both bound and resonance states, one should use quasi-complete basis sets. Yet, the use of large and dense basis sets is ineffective and highly impractical. In addition, the above-mentioned complex scaling method is unsuitable for a molecular analysis. Not long ago, an evidence that a mixed complex-scaled basis set can serve as a solution to the problem was presented by White et al., however, the behaviour of the bound states was not investigated systematically. In this work, we...

Resonances are metastable states that decay after a finite period of time. These states play a role in many physical processes. For example, in recent cold collision experiments, autoionization from a resonance state was observed. Complementing such observations with theory provides insight into the reaction dynamics under study. Theoretical investigation of autoionization processes is enabled via complex potential energy surfaces (CPESs), where the real and imaginary parts, respectively, provide the energy and decay rate of the system. Unfortunately, calculation of ab initio polyatomic CPESs are cumbersome; hence, they are not in abundance. Here, we present an ab initio polyatomic CPES utilizing a recently developed approach, which makes such calculations feasible. This CPES helps interpret the autoionization process observed in the He(23S) + H2 collision. From the behavior of the calculated CPES we can conclusively determine the nature of the autoionization process. Moreover, this CPES was used to gener...

Situations in which a molecule in a given configuration is electronically bound while in another configuration is autoionized are widespread in nature. In these situations, the change in molecular configuration due to nuclear dynamics is the reason the molecule emits free electrons to the surrounding, ie, autoionizes. Such a situation may even happen to molecules in their ground electronic state, for example, it can happen to H 2 − : at some bond lengths, the molecule is autoionized, at some bond lengths its ground state is bound, and at sufficiently large internuclear distances a stable hydrogen atom and a stable negative charged hydrogen, H − , in their ground electronic states, are obtained. In addition, such situations can be seen in electronic scattering from molecules and in cold molecular collisions. For example, in a collision between electronically excited helium atom and a hydrogen molecule in its ground state, metastable complex He*–H 2 is formed. As time passes this complex decays to helium in its ground state, H 2 + , and a free electron. In all these cases the molecular dynamics play a key role as the molecules are autoionized. This poses a problem, since the Born–Oppenheimer (BO) approximation is applicable only when the decay process due to ionization is ignored. Therefore, in order to study molecular dynamics and take autoionization into consideration, one should calculate the potential energy surfaces (PES) by imposing outgoing boundary conditions (OBCs) on the electronic wavefunctions. Doing so, the electronic molecular spectrum will be discrete (no continuum), where the PES will be either real (bound electronic states) or complex (metastable molecules that ionize). These complex potential energy surfaces (CPES) are what enables one to take into consideration the electronic autoionization in the molecular dynamics. Nevertheless, calculating CPES by standard quantum chemistry packages (SQCPs) is not a trivial task, since they were designed to calculate bound electronic excited states. Bound states lie on the real plane, unlike metastable states (resonances); therefore, explicit calculation of resonances requires modification of SQCPs. Several different possibilities for calculating CPES by modifying SQCPs are discussed in this review. Yet, the holy grail is to be able to use SQCPs, which are highly efficient codes, for calculating resonances without changing the codes. The main focus of this review will be on new methods, we have developed, that enable calculating CPESs from SQCPs, ie, without any modifications of standard codes. Such methods allow the calculations of polyatomic CPESs, as indicated by our preliminary results.

Atomic and molecular resonances play a role in many physical processes. Resonances are metastable states that have a finite lifetime. Nowadays, resonance complex eigenvalues can be calculated by quantum chemistry packages modified to include complex absorbing potentials (CAPs), where the imaginary energy part corresponds to the resonance lifetime. CAPs provide similar conditions to the ones obtained by imposing outgoing boundary conditions (OBCs), however, they also introduce artificial reflections. In this study, we present a scheme that eliminates the artificial effect of CAPs from bona fide electronic-structure calculations using the Padé approximant. This allows us to reach the physical limit and obtain the same eigenvalues as if we were able to solve the time-independent Schrödinger equation with OBCs (and without adding an unphysical CAP). We apply this scheme to the CO

Current experimental and theoretical studies on the effect of intermolecular interactions on molecular conduction appear to be in conflict with each other. In particular, some experimental results, e.g., the observation of 2-dimensional free-particle character for interface bound electrons indicate strong intermolecular interactions while other observations indicate an additive character of conduction properties. In this paper we use a generic tight binding model with a physically motivated choice of parameters in order to examine this issue. The model encompasses direct intermolecular interactions as well as through-metal interactions and can be solved exactly to yield spectral properties (surface density of states) and transport characteristics (transmission coefficients and current-voltage behaviors) for single molecule junctions, molecular islands and molecular layers. We find linear scaling of conduction properties with the number of conducting molecules in junctions characterized by molecular layers when the probe (STM tip) addresses different numbers of molecules; however, the conduction per molecule can differ significantly from that of an isolated single molecule. When a junction involves finite molecular islands of varying sizes, linear scaling sets in only beyond a certain molecular island size, of the order of a few tens of molecules. Implications for current observation of linear scaling behaviors are discussed., 25 pages, 8 figures. Journal of Computational and Theoretical Nanoscience, in press

Complex eigenvalues, resonances, play an important role in a large variety of fields in physics and chemistry. For example, in cold molecular collision experiments and electron scattering experiments, autoionizing and predissociative metastable resonances are generated. However, the computation of complex resonance requires modifications of standard electronic structure codes and methods, which are not always straightforward, in addition, application of complex codes requires more computational efforts. Here we show how resonance eigenvalues, positions and widths, can be calculated using the standard, widely used, electronic-structure packages. Our method enables the calculations of the complex resonance eigenvalues by using analytical continuation procedures (such as Padé). The key point in our approach is the existence of narrow analytical passages from the real axis to the complex energy plane. In fact, the existence of these analytical passages relies on using finite basis sets. These passages become narrower as the basis set becomes more complete, whereas in the exact limit, these passages to the complex plane are closed. As illustrative numerical examples we calculated the autoionization Feshbach resonances of helium, hydrogen anion, and hydrogen molecule. We show that our results are in an excellent agreement with the results obtained by other theoretical methods and with available experimental results.

International audience; A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Moller-Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr-2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

Potential functions of the ground and low excited states of Al2 are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. 3ÃŽÂ u is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the Λ = 1, 2 states lying 32.5 and 66.1 cm−1, respectively, above the Λ = 0 minimum (experimental values are 30.4 and 63.4 cm−1). The bond is somewhat too weak, with De 0.14 eV below experiment, Re too high by 0.08 ˚A, and Ée 21 cm−1 too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations.

The electronic levels of thorium and eka-thorium (element 122) are calculated in the framework of the Dirac-Coulomb-Breit Hamiltonian using a large Gaussian-spinor basis. Correlation is included by the Fock-space or intermediate Hamiltonian coupled-cluster method. The 51 reported levels of thorium and its ions are compared with experiment, giving an average error of 0.062 V for Fock space and 0.051 V for the intermediate Hamiltonian method. Predicted E122 levels are expected to have similar accuracy. The ground state of E122 is 8s27d8p, to be contrasted with 7s26d2 for Th. Increased relativistic effects in the super-heavy element lead to major differences between the level structure of these two atoms and their ions. The effects of Breit and QED terms are discussed.

The intermediate Hamiltonian Fock-space coupled cluster method developed recently is applied to excitations in the one-hole one-particle sector, taking xenon and radon atoms as test cases. Virtual orbitals are modified to yield better approximations to orbitals occupied in excited states. The usual Fock-space coupled cluster scheme diverges for these systems, but the intermediate Hamiltonian approach converges for large P spaces and yields excitation energies in very good agreement with experiment. The average error in the calculated values for the lowest excitation energies (about 20 for each atom) is 0.6%. Predictions are made for the unobserved 8s Rydberg states of Rn.

Electron affinities of the alkali atoms sodium to eka-francium are calculated by the intermediate Hamiltonian Fock-space coupled cluster approach, which allows very large P spaces. Large basis sets are used (37s32p23d18f10g7h for most atoms), and many electrons are correlated (from 10 for Na− to 52 for E119−) to account for core polarization. While the usual Fock-space method gives errors of 5%–9% for K, Rb, and Cs, the intermediate Hamiltonian results agree with all known values to 5 meV or 1%. The EA of Fr, not known experimentally, is predicted at 491±5 meV. While EAs decrease from Li to Cs, the Fr value is 20 meV higher than that of Cs, with E119 EA being much higher at 662 meV. This trend reversal is due to relativistic stabilization of s orbitals, which has been shown [Eliav et al., Phys. Rev. Lett. 74, 1079 (1995)] to give the rare gas E118 positive electron affinity.

The electronic level structure of eka-lead (element 114), the synthesis of which was reported last year, is studied by the recently developed intermediate Hamiltonian Fock-space coupled-cluster method. Very large basis sets are used, with l up to 8, and 36 electron are correlated. The accuracy of the resulting transition energies is tested by applying the same method to Pb; calculated ionization potentials and excitation energies agree with experiment within a few hundredths of an eV, and similar accuracy is expected for the heavier element. Ionization potentials and excitation energies of E114 are considerably higher than for Pb, due to the relativistic stabilization of the 7s and 7p1/2 orbitals. This indicates that eka-lead will probably be more inert and less metallic than lead.

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and co-workers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multireference coupled cluster schemes. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Energies are given for low-lying states of Ra which have not been observed experimentally.

An intermediate Hamiltonian Fock-space coupled-cluster method is presented, following the formalism developed by Malrieu in the context of perturbation theory. The method is expected to be applicable to many states not accessible by traditional FSCC. A pilot application to a large number of excited states of Sc + shows good convergence and agreement with experiment to a few hundredths of an eV, whereas the usual FSCC iterations diverge for all but the few lowest states.

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

We report high-level ab initio calculations and single-photon ionization mass spectrometry study of ionization of adenine (A), thymine (T), cytosine (C), and guanine (G). For thymine and adenine, only the lowest-energy tautomers were considered, whereas for cytosine and guanine we characterized the five lowest-energy tautomeric forms. The first adiabatic and several vertical ionization energies were computed using the equation-of-motion coupled-cluster method for ionization potentials with single and double substitutions. Equilibrium structures of the cationic ground states were characterized by DFT with the ωB97X-D functional. The ionization-induced geometry changes of the bases are consistent with the shapes of the corresponding molecular orbitals. For the lowest-energy tautomers, the magnitude of the structural relaxation decreases in the following series, GCAT, the respective relaxation energies being 0.41, 0.32, 0.25, and 0.20 eV. The computed adiabatic ionization energies (8.13, 8.89, 8.51-8.67, and 7.75-7.87 eV for A, T, C, and G, respectively) agree well with the onsets of the photoionization efficiency (PIE) curves (8.20 ± 0.05, 8.95 ± 0.05, 8.60 ± 0.05, and 7.75 ± 0.05 eV). Vibrational progressions for the S(0)-D(0) vibronic bands computed within double-harmonic approximation with Duschinsky rotations are compared with previously reported experimental photoelectron spectra and differentiated PIE curves.

The frozen natural orbital (FNO) approach, which has been successfully used in ground-state coupled-cluster calculations, is extended to open-shell ionized electronic states within equation-of-motion coupled-cluster (EOM-IP-CC) formalism. FNOs enable truncation of the virtual orbital space significantly reducing the computational cost with a negligible decline in accuracy. Implementation of the MP2-based FNO truncation scheme within EOM-IP-CC is presented and benchmarked using ionized states of beryllium, dihydrogen dimer, water, water dimer, nitrogen, and uracil dimer. The results show that the natural occupation threshold, i.e., percentage of the total natural occupation recovered in the truncated virtual orbital space, provides a more robust truncation criterion as compared to the fixed percentage of virtual orbitals retained. Employing 99%-99.5% natural occupation threshold, which results in the virtual space reduction by 70%-30%, yields errors below 1 kcal/mol. Moreover, the total energies exhibit linear dependence as a function of the percentage of the natural occupation retained allowing for extrapolation to the full virtual space values. The capabilities of the new method are demonstrated by the calculation of the 12 lowest vertical ionization energies (IEs) and the lowest adiabatic IE of guanine. In addition to IE calculations, we present the scans of potential energy surfaces (PESs) for ionized (H(2)O)(2) and (H(2))(2). The scans demonstrate that the FNO truncation does not introduce significant nonparallelity errors and accurately describes the PESs shapes and the corresponding energy differences, e.g., dissociation energies.

Our recent calculation of the effect of intermolecular interactions on molecular conduction (J. Comput. Theor. Nanosci. 2008, 5, 535) is generalized to molecules adsorbed on a model semiconductor surface and in a metal-molecule-semiconductor junction. The metal and semiconductor electrodes are represented by cubic lattices within generic tight binding models, where the semiconductor two-band structure is described by using a simple site-alteration property. A physically motivated choice of parameters for the molecule(s) and the electrodes completes the model definition. The model encompasses direct intermolecular interactions as well as through-metal interactions and can be solved exactly to yield spectral properties (surface density of states) and transport characteristics (transmission coefficients and current-voltage behavior) for single-molecule junctions and molecular layers. The model is applied to analyzing the effect of intermolecular interactions on the predicted negative differential resistance in metal-molecule-semiconductor junctions (recently observed in scanning tunneling microscopy studies of adsorbates on Si(100)).

An alternative formulation of the intermediate Hamiltonian Fock-space coupled cluster scheme developed before is presented. The methodological and computational advantages of the new formulation include the possibility of using a model space with determinants belonging to different Fock-space sectors. This extends the scope of application of the multireference coupled cluster method, and makes possible the use of quasiclosed shells (e.g., p2, d4) as reference states. Representative applications are described, including electron affinities of group-14 atoms, ionization potentials of group-15 elements, and ionization potentials and excitation energies of silver and gold. Excellent agreement with experiment (a few hundredths of an electronvolt) is obtained, with significant improvement (by a factor of 5-10 for p3 states) over Fock-space coupled cluster results. Many states not reachable by the Fock-space approach can now be studied.

High-accuracy ground- and excited-state energies of heavy and superheavy atoms are calculated in the framework of the Dirac-CoulombBreit Hamiltonian. Electron correlation is treated by the Fock-space coupled cluster method. Several variants of the recently developed intermediate Hamiltonian approach are also described. These schemes make possible much larger P (model) spaces, which may be varied to convergence without encountering intruder state problems, thus enhancing accuracy and allowing application to states not accessible before. In particular, the mixed-sector IH scheme suppresses intruder states coming from higher Fock space sectors, making it possible to use quasi-closed shells (p2, d4 etc.) as reference. Very large basis sets, going up to l= 8, are used. The outer 20–40 electrons are correlated. Representative applications are described, showing excellent agreement with experimentally known transition energies of heavy atoms, usually within a few hundredths of an eV. This makes possible reliable predictions for superheavy elements, found to possess chemical and spectroscopic properties significantly different from their lighter homologues.

High-accuracy results for energy levels of heavy and superheavy atoms are presented. The projected (or no-virtual-pair) Dirac-Coulomb-Breit Hamiltonian serves as the starting point and defines the physical framework. One-electron four-component Dirac-Fock-Breit functions, similar in spirit to Hartree-Fock orbitals in the nonrelativistic formulation, are calculated first, followed by treatment of electron correlation. Correlation is included by the Fock-space coupled cluster method. The recent intermediate Hamiltonian approach makes it possible to use larger and more flexible P (model) spaces, thereby extending the range of applicability to states not accessible before. Accuracy is greatly improved for systems which can be treated by both methods, and the model space structure can be studied and pushed to convergence for the first time. Applications address mostly transition energies (ionization potentials, excitation energies, electron affinities) in various atoms. Very large basis sets, going up to l = 8, are used. High- l orbitals are particularly important for transitions involving ƒ electrons. The outer 20-40 electrons of the atom are correlated. The Breit term is required for fine-structure splittings and for ƒ transitions. Representative applications are described, including electron affinities of alkali atoms, obtained within 5 meV of known experimental values and providing the best estimate of the experimentally unknown EA of francium; the gold atom, with relativistic effects of 3-4 eV on transition energies; and Pr 3+ , where the many f 2 levels are reproduced with great precision. The most exciting aspect of the high accuracy provided by the method is the ability to obtain reliable predictions for superheavy elements, where level ordering (and therefore chemistry) may differ from that of the lighter homologues. Thus, the ground state of eka-gold (E111) is 6 d 9 7 s 2 , rather than the 6 d 10 7 s expected from other group-11 elements; in Rf (E104), opposite effects of relativity and correlation lead finally to a 7 s 2 6 d 2 ground state, ∼0.3 eV below the 7 s 2 6 d 7 p predicted by MCDF; eka-lead (E114), a potential member of the “island of stability” forecast by nuclear physics, is predicted to have ionization potentials higher than all other group-14 atoms except carbon; and eka-radon (E118) has a unique property for a rare gas, binding an electron with an affinity of −0.064(2) eV. QED corrections are calculated for the latter property, reducing the binding energy of the 8 s electron by 0.0059(5) eV or 9%, the largest relative QED effect reported for a neutral or weakly ionized species.

Four-component methods for high-accuracy atomic calculations are reviewed. The projected (or no-virtual-pair) Dirac-Coulomb-Breit Hamiltonian serves as the starting point and defines the physical framework. One-electron four-component Dirac-Fock-Breit functions, similar in spirit to Hartree-Fock orbitals in the nonrelativistic formulation, are calculated first, followed by treatment of electron correlation. Correlation methods include multiconfiguration Dirac-Fock and many-body perturbation theory or its all-order limit, the coupled cluster approach. The Fock-space CC and its extension to the intermediate Hamiltonian approach are described. Applications address mostly transition energies in various atoms. Very large basis sets, going up to l = 8, are used. High l orbitals are particularly important for transitions involving f electrons. The Breit term is required for fine-structure splittings and for f transitions. Representative applications are described, including the gold atom, with relativistic effects of 3–4 eV on transition energies; eka-gold (E111), where relativity changes the ground state from 6d 107s to 6d 97s 2; Pr3+, where the many f 2 levels are reproduced with great precision; Rf (E104), where opposite effects of relativity and correlation lead finally to a 7s 26d 2 ground state, ~0.3 eV below the 7s 26d7p predicted by MCDF; eka-lead (E114), a potential member of the “island of stability” forecast by nuclear physics, predicted to have ionization potentials higher than all other group-14 atoms except carbon; and eka-radon (E118), which has a unique property for a rare gas, positive electron affinity. Heavy anions are described, showing instances of multiple stable excited states. Finally, applications to properties other than energy are discussed.

An intermediate Hamiltonian Fock-space coupled cluster method is presented. This method allows the use of large and flexible P spaces without encountering intruder-state problems. The larger P spaces enhance the accuracy of calculated transition energies by factors of 3–6, and make accessible many states which could not be handled by other CC methods. Examples given include the pilot calculation on Sc + levels, where accuracy increased by a factor of 4; element 114, where ionisation potentials show considerable increase relative to lighter group-14 atoms, due to relativistic stabilisation of the 7s and 7p1/2 orbitals; and a benchmark calculation of the electron affinities of the alkali atoms Na–E119, where results agree within 5 meV or better with known experimental values, providing a new reference value of 491±5 meV for the experimentally unknown EA of Fr.

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and coworkers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multi-reference coupled cluster approaches. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. While Malrieu's formulation eliminated Pm → Pi transitions up to third order only, the requirement introduced here that Pm → Q amplitudes of the two excitation operators be equal makes possible an all-order method without these dangerous transitions. This requirement is shown to be satisfied for sufficiently large Pi. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Excellent agreement with experiment (better than 0.01 eV) is obtained for the electron affinities of alkali atoms, and excitation energies of Xe and Rn, not accessible by the traditional coupled-cluster Fock-space method, are calculated showing high accuracy.