Showing papers on "Coupled cluster published in 2002"

Estimates of the Ab Initio Limit for π−π Interactions: The Benzene Dimer

Abstract: State-of-the-art electronic structure methods have been applied to the simplest prototype of aromatic π−π interactions, the benzene dimer. By comparison to results with a large aug-cc-pVTZ basis set, we demonstrate that more modest basis sets such as aug-cc-pVDZ are sufficient for geometry optimizations of intermolecular parameters at the second-order Moller−Plesset perturbation theory (MP2) level. However, basis sets even larger than aug-cc-pVTZ are important for accurate binding energies. The complete basis set MP2 binding energies, estimated by explicitly correlated MP2−R12/A techniques, are significantly larger in magnitude than previous estimates. When corrected for higher-order correlation effects via coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], the binding energies De (D0) for the sandwich, T-shaped, and parallel-displaced configurations are found to be 1.8 (2.0), 2.7 (2.4), and 2.8 (2.7) kcal mol-1, respectively.

Transition moments and excited-state first-order properties in the coupled-cluster model CC2 using the resolution-of-the-identity approximation

Abstract: An implementation of transition moments and excited-state first-order properties is reported for the approximate coupled-cluster singles-and-doubles model (CC2) using the resolution of the identity (RI) approximation. In parallel to the previously reported code for the ground- and excited-state amplitude equations, we utilize a partitioned form of the CC2 equations and thus eliminate the need to store any N 4 intermediates. This opens the perspective for applications on molecules with 30 and more atoms. The accuracy of the RI approximation is tested for a set of 29 molecules for the aug-cc -p V X Z (X=D,T,Q) basis sets in connection with the recently optimized auxiliary basis sets. These auxiliary basis sets are found to be sufficient even for the description of diffuse states. The RI error is compared to the usual basis set error and is demonstrated to be insignificant.

Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches

Abstract: The recently developed new approach to the many-electron correlation problem in atoms and molecules, termed the method of moments of coupled-cluster (CC) equations (MMCC), is reviewed. The ground-state MMCC formalism and its extension to excited electronic states via the equation-of-motion coupled-cluster (EOMCC) approach are discussed. The main principle of all MMCC methods is that of the non-iterative energy corrections which, when added to the ground- and excited-state energies obtained in the standard CC calculations, such as CCSD or EOMCCSD, recover the exact, full configuration interaction (CI) energies. Three types of the MMCC approximations are reviewed in detail: (i) the CI-corrected MMCC methods, which can be applied to ground and excited states; (ii) the renormalized and completely renormalized CC methods for ground states; and (iii) the quasi-variational MMCC approaches for the ground-state problem, including the quadratic MMCC models. It is demonstrated that the MMCC formalism provides a new ...

A general state-selective multireference coupled-cluster algorithm

Abstract: A state-selective multireference coupled-cluster algorithm is presented which is capable of describing single, double (or higher) excitations from an arbitrary complete model space. One of the active space determinants is chosen as a formal Fermi-vacuum and single, double (or higher) excitations from the other reference functions are considered as higher excitations from this determinant as it has been previously proposed by Oliphant and Adamowicz [J. Chem. Phys. 94, 1229 (1991)]. Coupled-cluster equations are generated in terms of antisymmetrized diagrams and restrictions are imposed on these diagrams to eliminate those cluster amplitudes which carry undesirable number of inactive indices. The corresponding algebraic expressions are factorized and contractions between cluster amplitudes and intermediates are evaluated by our recent string-based algorithm [J. Chem. Phys. 115, 2945 (2001)]. The method can be easily modified to solve multireference configuration interaction problems. Performance of the method is demonstrated by several test calculations on systems which require a multireference description. The problem related to the choice of the Fermi-vacuum has also been investigated.

Low-order scaling local electron correlation methods. V. Connected triples beyond (T): Linear scaling local CCSDT-1b

Abstract: A new O(N ) method for the iterative treatment of connected triple substitutions in the framework of local coupled cluster theory is introduced here, which is the local equivalent of the canonical CCSDT-1b method. The effect of the triple substitutions is treated in a self-consistent manner in each coupled cluster iteration. As for the local (T) method presented earlier in this series the computational cost of the method scales asymptotically linear with molecular size. The additional computational burden due to the involvement of triples in each coupled cluster iteration hence is not nearly as dramatic as for the parental canonical method, where it implies an increase in the computational complexity of the coupled cluster iteration from O(N6) to O(N7). The method has certain advantages in comparison to the perturbative a posteriori treatment of connected triples (T) for cases where static correlation effects start to play a role. It is demonstrated that molecules with about 100 atoms and 1000 basis funct...

Linear scaling local correlation approach for solving the coupled cluster equations of large systems.

Abstract: A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.

A new, fast, semi-direct implementation of linear scaling local coupled cluster theory

Abstract: A new way to compute the external exchange matrices in the local coupled cluster (LCC) theory is presented, which eliminates the most important bottleneck of our previous linear scaling LCC methods. It is based on a decomposition of the transformed two-electron integral set involving four external indices into blocks belonging to quadruples of atoms. A new additional transformation module was developed, which generates this very compact 4-external integral set before the LCC iteration loop is entered. The length of this integral set and the computational cost for producing it scale linearly with molecular size. Using these precomputed integrals, their contraction with the amplitudes, i.e. the assembly of the external exchange matrices occurring in each LCC iteration now is performed directly in the (external) space of the projected AOs (AOs, atomic orbitals) rather than in AO basis as previously, and proceeds exceedingly fast (3 min compared to 15 h with our previous algorithm, for the largest test-molecule considered in this paper).

Helium dimer dispersion forces and correlation potentials in density functional theory.

Abstract: The dispersion interaction in the helium dimer is considered from the viewpoint of the force on a nucleus. At large internuclear separations, Brueckner coupled cluster BD(T) forces agree well with near-exact dispersion forces. The atomic density distortion associated with the dispersion force is quantified by comparing the BD(T) dimer density with a superposition of atomic densities. For density functional theory calculations in the Hartree-Fock-Kohn-Sham (HFKS) formalism, the accuracy of the dispersion force is governed by the correlation potential. Calculations using the conventional Lee-Yang-Parr [Phys. Rev. B 37, 785 (1988)] potential only generate a small density distortion, giving forces significantly smaller than BD(T). The BD(T) electron densities are therefore used to determine improved correlation potentials using a modified Zhao-Morrison-Parr (ZMP) approach [Phys. Rev. A 50, 2138 (1994)]. HFKS calculations using these ZMP potentials quantitatively reproduce the distortion, giving dispersion forces in good agreement with BD(T). The dimer ZMP correlation potential is partitioned into two parts, one equal to the sum of two unperturbed spherical atomic correlation potentials and the other representing an interaction potential. HFKS calculations using the former do not generate the distortion; forces are close to Hartree-Fock. Calculations using the latter do generate the distortion, giving forces essentially identical to those from the full dimer potential. The origin of the distortion is traced to the asymmetric structure of the interaction correlation potential in the vicinity of each nucleus.

Comparison of multireference Møller-Plesset theory and time-dependent methods for the calculation of vertical excitation energies of molecules

Abstract: The vertical singlet-singlet excitation energies for a benchmark set of 14 medium and large molecules have been investigated with three quantum chemical methods. Calculations for electronic states with very different character in organic and inorganic systems are used to assess the accuracy and applicability of a simplified multireference Miller-Plesset (MR-MP2) approach, time-dependent density functional theory (TDDFT), and an approximate coupled cluster method with single and double excitations (CC2). In the pure ab initio approaches the resolution of the identity (RI) method for the calculation of the two-electron integrals is used to improve computational efficiency. It is shown that independently of the complexity of the electronic states involved, only the MR-MP2 method yields high accuracy (mean absolute deviation of 0.14 eV for 22 states). This finding is of particular importance because our scheme avoids computationally demanding orbital optimization steps and employs very compact reference wave functions. The TDDFT results are significantly poorer (mean absolute deviation of 0.26 eV), and systematic deviations for some π → π* states, Rydberg states, and systems with unusual electronic structure are obtained. It is concluded that TDDFT has a potential for exploratory investigations or for very large molecules due to its computational efficiency. The CC2 method shows a tendency to overestimate excitation energies and is also limited to systems where the ground state is well described by a single determinant.

Implementation of RI-CC2 triplet excitation energies with an application to trans-azobenzene

Abstract: Triplet excitation energies within the approximate coupled cluster singles and doubles model CC2 have been implemented using an explicitly spin coupled basis and the resolution of the identity approximation for two-electron integrals. This approach reduces substantially the requirements for CPU time, disk space and memory, and extends the applicability of CC2 for triplet excited states to molecules that could not be studied before with this method. We report an application to the lowest singlet and triplet vertical excitation energies of trans-azobenzene. An accurate ab initio geometry optimized at the MP2/cc-pVTZ level is presented, and CC2 calculations in the aug-cc-pVTZ basis set with 874 basis functions are combined with coupled cluster singles and doubles (CCSD) calculations in modest basis sets to obtain the best possible estimates for the vertical excitation energies. The results show that recently reported SOPPA calculations are unreliable. Good agreement with experiment is obtained for the lowest excited singlet state S1, but for the lowest triplet state T1 the results indicate a large difference between the vertical excitation energy and the experimentally observed transition.

The QM/MM approach for wavefunctions, energies and response functions within self-consistent field and coupled cluster theories

Abstract: This paper presents the coupled cluster/molecular mechanics (CC/MM) and self-consistent field/molecular mechanics (SCF/MM) approaches for wavefunctions, energies and response properties. Two physically different theories are derived, the mean-field and the direct-field interaction approaches, together with expressions for the optimization condition of both variational and non-variational wavefunctions and energies. Also derived are the linear response functions at the CC/MM and SCF/MM levels of theory, and the expressions are compared with the vacuum response functions.

Electron excitation energies using a consistent third-order propagator approach: Comparison with full configuration interaction and coupled cluster results

Abstract: A recently developed consistent third-order propagator method for the treatment of electronic excitation in molecules is tested in first applications. The method referred to as third-order algebraic-diagrammatic construction [ADC(3)] extends the existing second-order approximation and aims at a more accurate computation of excitation energies and transition moments than afforded at the second-order level. For a stringent test of the method we compare the ADC(3) energies for over 40 singlet and triplet vertical transitions in H2O, HF, N2, and Ne with the results of recent full configuration interaction (FCI) and coupled cluster (CC) computations. The ADC(3) results reflect a substantial and uniform improvement with respect to the second-order description. The mean absolute deviation of the single excitation energies from the FCI results is below 0.2 eV. Although this does not equal the accuracy of the third-order CC3 model, the ADC(3) method, scaling as N6 with the number of orbitals, may be viewed as a good compromise between accuracy and computational cost.

Relative Stabilities of Three Low-Energy Tautomers of Cytosine: A Coupled Cluster Electron Correlation Study

Abstract: High-level quantum chemical calculations have been carried out in an effort to reinvestigate the relative stabilities of the three lowest-lying tautomers of cytosine. Geometries were optimized at the CCSD/TZP level and electronic energies calculated at CCSD(T)/cc-pVTZ and vibrational frequencies at MP2/TZP. Comparative DFT calculations were also performed. From these data Gibbs free energies and equilibrium mole ratios were calculated. In agreement with most previous theoretical and experimental results, the amino−hydroxy tautomer 2b was found to be the most stable structure. As a new result, the amino−oxo form 1 and the imino−oxo form 3a have very nearly the same electronic energy, about 1.5−1.7 kcal/mol above 2b. The calculated ΔG values at standard temperature are ∼0.8 kcal/mol relative to 2b, again for both 1 and 3a. These results about the stability of the oxo form 1 are in quantitative agreement with experimental estimates in the literature, both from matrix isolation infrared and from molecular bea...

Analytic second derivatives for the full coupled-cluster singles, doubles, and triples model: Nuclear magnetic shielding constants for BH, HF, CO, N2, N2O, and O3

Abstract: An implementation of analytic second derivatives for the coupled-cluster singles, doubles, and triples (CCSDT) model is reported and applied to the calculation of nuclear magnetic shielding constants of BH, HF, CO, N2, N2O, and O3. The CCSDT calculations yield further evidence for the high accuracy provided by chemical shift calculations employing the coupled-cluster singles, doubles (CCSD) approach augmented by a perturbative triples correction [CCSD(T)].

Low-lying potential energy surfaces

Abstract: Preface 1. Overview: Accurate Description of Low-Lying Electronic States and Potential Energy Surfaces 2. Simultaneous Account of Dynamic and Nondynamic Correlations Based on Complementarity of CI and CC Approaches 3. Method of Moments of Coupled-Cluster Equations: A New Theoretical Framework for Designing "Black-Box" Approaches for Molecular Potential Energy Surfaces 4. The Photoelectron Spectrum of the NO3 Radical Revisited: A Theoretical Investigation of Potential Energy Surfaces and Conical Intersections 5. Coupled Cluster Methods for Bond-Breaking 6. State-Specific Multireference Coupled Cluster-Based Methods for Potential Energy Surfaces and Their Approximate Variants 7. The Excited and Ion States of Allene 8. Hamiltonian Matrix Elements for the Table-CI Method Using Genealogical Configuration State Functions 9. Jacob's Ladder for Time-Dependent Density-Functional Theory: Some Rungs on the Way to Photochemical Heaven 10. Spectral Theory of Chemical Bonding 11. Comparison of CaF, ZnF, CaO, and ZnO: Their Anions and Cations in Their Ground and Low-Lying Excited States 12. The X1(2(3/2) and X2(2(1/2) Potentials of the Halogen Monoxides: A Comparison of RKR and Ab Initio Results 13. Symmetry in Spin-Orbit Coupling 14. Non-Adiabatic Bending Dissociation of OCS Induced by Orbital Unlocking 15. Electronic Structure and Dynamics in the O4 System 16. Model Studies of Intersystem Crossing Effects in the O + H2 Reaction 17. The Challenge of High-Resolution Dynamics: Rotationally Mediated Unimolecular Dissociation of HOCl 18. The Electronic Adiabatic-to-Diabatic Transformation Matrix and the Irreducible Representation of the Rotation Group 19. Spectroscopic Determination of Potential Energy Surfaces for the Out-of-Plane Ring Vibrations of Indan and Related Molecules in Their S0 and S1 ((, (*) States 20. Semiclassical Time Evolution in the Forward-Backward Stationary-Phase Limit 21. Development and Application of an Ab Initio Methane-Water Potential for the Study of Phase Equilibria of Methane Hydrates Indexes Author Index Subject Index

Energy profile of the interconversion path between T-shape and slipped-parallel benzene dimers

Abstract: The energy profile of the interconversion path between the T-shape and slipped-parallel dimers has been studied by high level ab initio calculations. The CCSD(T) (coupled cluster calculation with single and double substitutions with noniterative triple excitations) interaction energy at the basis set limit has been estimated from the MP2 (the second-order Moller–Plesset calculation) interaction energy near the basis set limit and the CCSD(T) correction term using the 6-311G* basis set. The calculated CCSD(T) level energy profile has shown that the potential is very flat and the interconversion barrier height is very small (around 0.2 kcal/mol). The MP2 calculations using large basis sets near the basis set limit considerably overestimate the attraction of the slipped-parallel dimer, which indicates the importance of higher level electron correlation correction for studying the potential energy surface of the benzene dimer.

Extension of the method of moments of coupled-cluster equations to excited states: The triples and quadruples corrections to the equation-of-motion coupled-cluster singles and doubles energies

Abstract: The recently proposed extension of the method of moments of coupled-cluster equations (MMCC) to excited states via the equation-of-motion coupled-cluster (EOMCC) formalism [K. Kowalski and P. Piecuch, J. Chem. Phys. 115, 2966 (2001)] is developed further. A new approximate variant of the excited-state MMCC theory, termed the MMCC(2,4) method, is proposed and tested. In the MMCC(2,4) method, relatively simple noniterative corrections due to triples and quadruples are added to the excited-state energies obtained in the standard EOMCCSD (EOMCC singles and doubles) calculations. The performance of the MMCC(2,4) approach is illustrated by the results of calculations for the excited states of N2, C2, and CH+. The MMCC(2,4) energies are compared with the results of the MMCC(2,3) calculations, in which noniterative corrections due to triples only are added to the EOMCCSD energies, and with the results of other EOMCC calculations, including various EOMCC triples schemes.

Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model

Abstract: The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.

To Multireference or not to Multireference: That is the Question?

Abstract: I present a personal viewpoint on multi-reference coupled-cluster theory, its pros and cons. I also suggest some criteria that should be satisfied by multi-reference CC, not the least of which is to develop a tool that will be (almost!) as easy to apply as today’s powerful array of single reference coupled-cluster methods. Some approaches like the equation of motion CC method offers a multi-reference description of some target states, while being entirely single reference in execution. Perhaps it offers a model for further generalization to a wider array of multi-reference problems.

Extrapolating the coupled-cluster sequence toward the full configuration-interaction limit

Abstract: Extrapolation methods that accelerate the convergence of coupled-cluster energy sequences toward the full configuration–interaction (FCI) limit are developed and demonstrated for a variety of atoms and small molecules for which FCI energies are available, and the results are compared with those from Moller–Plesset (MP) perturbation theory. For the coupled-cluster sequence SCF, CCSD, CCSD(T), a method based on a continued-fraction formalism is found to be particularly successful. It yields sufficient improvement over conventional CCSD(T) that the results become competitive with, and often better than, results from the MP4-qλ method (MP4 summed with quadratic approximants and λ transformation). The sequence SCF, CCSD, CCSDT can be extrapolated with a quadratic approximant but the results are not appreciably more accurate than those from the CCSD(T) continued fraction. Singularity analysis of the MP perturbation series provides a criterion for estimating the accuracy the CCSD(T) continued fraction.

Formulation and implementation of the full coupled-cluster method through pentuple excitations

Abstract: Using the quasilinearized formulation of CC theory in terms of recursively computed intermediates, we present the detailed equations and implementation of coupled-cluster theory with single, double, triple, quadruple, and pentuple excitations, CCSDTQP. We illustrate its results by comparison with several full CI results in double zeta, polarized basis sets (DZP), at different geometries. The maximum error compared to full CI occurs for H2O at twice Re which is 0.026 mH. For all other cases, HF, SiH2, and CH2 in its singlet state, the largest errors are 0.001 mH. The magnitude of the connected T5 contribution is as large as 0.35 mH, but usually less than 0.1 mH for these examples.

Eigenvalues, integer discontinuities and NMR shielding constants in Kohn-Sham theory

Abstract: Kohn—Sham eigenvalues are determined from coupled cluster electron densities. The calculated HOMO—LUMO eigenvalue differences are compared with those from conventional generalized gradient approximation (GGA) exchange-correlation functionals for a range of small molecules. In all cases, GGA HOMO—LUMO differences are smaller than those calculated from the coupled cluster densities. When the GGA HOMO—LUMO differences are explicitly corrected—such that they equal those calculated from electron densities—significant improvements in NMR shielding constants are obtained. The eigenvalues calculated from electron densities are also used to approximate the magnitude of the integer discontinuity in the exact exchange-correlation potential. The value of the Kohn—Sham HOMO eigenvalue is then considered. Although HOMO eigenvalues from high quality, asymptotically vanishing, exchange-correlation potentials are close to the negative of the ionization potential, HOMO eigenvalues from the GGA functionals are shifted upwar...

Vibrational energies for NH3 based on high level ab initio potential energy surfaces

Abstract: Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple substitutions [CCSD(T)] have been carried out to generate six-dimensional (6D) potential energy surfaces (PES) and dipole moment surfaces (DMS) for the electronic ground state of ammonia Full 6D-PES and 6D-DMS (14400 points) were computed with the augmented correlation-consistent triple-zeta basis (aug-cc-pVTZ) For a selected number of points (420 in C3v symmetry and 1260 in lower symmetry), more accurate energies (CBS+) were obtained by extrapolating the CCSD(T) results for the aug-cc-pVXZ (X=T,Q,5) basis sets to the complete basis set limit and adding corrections for core-valence correlation and relativistic effects Two procedures were investigated to enhance the quality of the 6D-PES from CCSD(T)/aug-cc-pVTZ by including the CBS+ data points The resulting 6D-PES were represented by analytical functions involving Morse variables for the stretches, symmetry-adapted bending coordinates, and a specially designed inversion coordinate (up to 76 fitted parameters, rms deviations of about 5 cm−1 for 14 400 ab initio data points) For these analytical surfaces, vibrational energies were calculated with a newly developed computer program using a variational model that employs an Eckart-frame kinetic energy operator Results are presented and compared to experiment for the vibrational band centers of NH3 and its isotopomers up to around 15 000 cm−1 For our best 6D-PES, the term values of the fundamentals are reproduced with rms deviations of 44 cm−1 (NH3) and 26 cm−1 (all isotopomers), the maximum deviation being 79 cm−1

State Selective Equation of Motion Coupled Cluster Theory: Some Preliminary Results

Abstract: A multireference variant of coupled cluster theory is described that applies to systems that can qualitatively be described by deleting two electrons from a closed shell determinant, for example biradicals, single bond breaking processes, or valence excited states. The theory can be generalized to arbitrary open-shell systems and takes a form that is akin to equation-of-motion coupled cluster theory, but where all wave function parameters are explicitly optimized for the state of interest. The implementation of the present methods was accomplished in an automated fashion using the recently developed Automatic Program Generator (APG). We present benchmark results for the O 2 and F 2 molecules and investigate the behaviour of a number of closely related variants within the same general framework. Keywords: Multireference electronic structure; Coupled cluster; Electronically excited states; Automatic code generation. I. Introduction Single reference coupled cluster theory, [1,2] especially CCSD(T) [3,4], is a highly successful approach to describe the electronic structure of systems that are qualitatively reasonably well described by a single determinant (many closed-shell molecules and high-spin open-shell systems) [5-8]. Likewise coupled cluster response theory (CCLRT [9-11]) and its cousin equation-of-motion coupled cluster theory (EOM-CC [5,12]) are well suited to describe singly excited states and radicals. An important prerequisite for the applicability of the CC response approach is the presence of a nearby state that can serve as the reference in the parent state CCSD calculation. Most commonly the reference state is a closed-shell system that differs by up to one electron from the states of interest. The

Introduction to modern methods of quantum many-body theory and their applications

Abstract: Density functional theory microscopic description of quantum liquids the coupled cluster method and its application experiments with a Rubidium Bose-Einstein condensate theoretical aspects of Bose-Einstein condensation elementary excitations and dynamic structure of quantum fluids theory of correlated basis functions the magnetic susceptibility of liquid 3He the hyperspherical harmonic method - a review and some recent developments the nuclear many-body problem.

First-order properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis

Abstract: An implementation is reported for first-order properties of excited triplet states within the approximate coupled cluster model CC2 using an explicitly spin coupled basis for the triplet excitation manifold and the resolution of the identity (RI) approximation for the electron repulsion integrals. Results are presented for the change of the second moment of charge upon excitation in the ππ* valence and n=3 Rydberg states of benzene. Employing large basis sets with up to 828 functions, we obtain results close to the CC2 basis set limit and are able to resolve an uncertainty in the assignment of the lowest 1E1u states. It is found that the often used %T1 measure for the single excitation contribution to excited states is not reliable for a comparison across different excitation operator manifolds. An alternative diagnostic is proposed which provides a unique measure for the single excitation contribution that is independent of the chosen representation of the excitation operator manifold.

Solvated electrons in very small clusters of polar molecules: (HF)3-

Abstract: Photoelectron spectra of (HF)(3)(-) reveal coexistence of two anionic isomers with vertical electron detachment energies (VDE) of 0.24 and 0.43 eV. The results of electronic-structure calculations, performed at the coupled cluster level of theory with single, double, and noniterative triple excitations, suggest that the two isomers observed experimentally are an open, zigzag, dipole-bound anion and an asymmetric solvated electron, in which the dipole-bound anion of (HF)(2) is solvated by one HF monomer at the side of the excess electron. The theoretical VDE of 0.21 and 0.44 eV, respectively, are in excellent agreement with the experimental data.