Showing papers in "Theoretical Chemistry Accounts in 2003"

Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree method

Abstract: Quantum molecular dynamics describes the time-evolution of a chemical system at the atomic level by directly solving the Schrodinger equation. Time-dependent methods, exemplified by wavepacket propagation, are by now developed to a point where they provide an important insight into the mechanism of many fundamental processes. Of these methods, the most versatile and efficient is probably the multi-configuration time-dependent Hartree (MCTDH) method. The form of the wavefunction used leads to a particularly compact description of the system, and it is possible to run either qualitative, cheap, or accurate, expensive calculations within the same framework. MCTDH has now shown that it is able to treat systems much larger than other wavepacket propagation methods, and benchmark calculations on systems with up to 24 degrees of freedom have been made. In contrast, standard methods can rarely treat more than 4–6 degrees of freedom. In the following, we review the basic theory of MCTDH. Recent advances are included, such as the development of the method for treating the time-evolution of density operators.

Resistance distance and Laplacian spectrum

Abstract: The resistance distance r ij between two vertices v i and v j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r ij ||.

Investigation of the S0S1 excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

Abstract: We have investigated the S0 and S1 electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin.

Similarities and differences in the structure of 3d-metal monocarbides and monoxides

Abstract: The structure and properties of the monocarbides ScC, TiC, VC, CrC, MnC, FeC, CoC, NiC, CuC, ZnC and their negatively and positively charged ions together with 3d-metal monoxide cations are calculated by density functional theory (DFT) and hybrid DFT methods. In addition to the spectroscopic constants, the computed properties include the electron affinities, ionization energies, and dissociation energies. These results along with our previous results for the neutral and negatively charged 3d-metal monoxides allow a detailed comparison of similarity and differences in the bonding of the metal oxides and carbides. These results are compared with results obtained using other theoretical approaches and with experiment. Chemical bonding, analyzed using the natural bond orbital scheme, was found to be rather different in the 3d-metal monocarbides and monoxides.

A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions

Abstract: A detailed derivation of the frozen-orbital second-order perturbation theory (MP2) analytic gradient in the spin-orbital basis is presented. The summation ranges and modification of the MP2 gradient terms that result from the frozen-orbital approximation are clearly identified. The frozen-orbital analytic gradients for unrestricted MP2 and closed-shell MP2 are determined from the spin-orbital derivation. A discussion of useful implementation procedures is included. Timings from full and frozen-orbital MP2 gradient calculations on the molecule silicocene (the silicon analog of the sandwich compound ferrocene) are also presented.

Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method

Abstract: Hybrid potentials have become a common tool in the study of many condensed-phase processes and are the subject of much active research. An important aspect of the formulation of a hybrid potential concerns how to handle covalent bonds between atoms that are described with different potentials and, most notably, those at the interface of the quantum mechanical (QM) and molecular mechanical (MM) regions. Several methods have been proposed to deal with this problem, ranging from the simple link-atom method to more sophisticated hybrid-orbital techniques. Although it has been heavily criticized, the link-atom method has probably been the most widely used in applications, especially with hybrid potentials that use semiempirical QM methods. Our aim in this paper has been to evaluate the link-atom method for ab initio QM/MM hybrid potentials and to compare the results it gives with those of previously published studies. Given its simplicity and robustness, we find that the link-atom method can produce results of comparable accuracy to other methods as long as the charge distribution on the MM atoms at the interface is treated appropriately.

Accuracy of geometries: Influence of basis set, exchange-correlation potential, inclusion of core electrons, and relativistic corrections

Abstract: The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

Abstract: A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH †† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH †† =20.1 kcal/mol, ΔH rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol.

Continuum solvation of large molecules described by QM/MM: a semi-iterative implementation of the PCM/EFP interface

Abstract: The direct inversion of the iterative subspace (DIIS) solution to the iterative integral equation formalism polarized continuum model (IEF–PCM, 2001 Theor. Chem. Acc. 105:1186) is applied to the effective fragment potential IEF–PCM interface (2002 J Chem Phys 116:5023). Compared to a direct matrix-inversion solution, the DIIS–PCM is up to an order of magnitude more efficient both in computing time and memory requirements for large systems. Multipole treatments of long-range electrostatic interactions further reduce the computing time by up to 50%. All the CPU intensive computations are parallelized. The data presented in this paper demonstrate that use of the iterative IEF–PCM is an efficient way to model bulk solvation of large biomolecules described by QM/MM.

Long-range and short-range Coulomb correlation effects as simulated by Hartree-Fock, local density approximation, and generalized gradient approximation exchange functionals

Abstract: Exchange functionals used in density functional theory (DFT) are generally considered to simulate long-range electron correlation effects It is shown that these effects can be traced back to the self-interaction error (SIE) of approximate exchange functionals An analysis of the SIE with the help of the exchange hole reveals that both short-range (dynamic) and long-range (nondynamic) electron correlation effects are simulated by DFT exchange where the local density approximation (LDA) accounts for stronger effects than the generalized gradient expansion (GGA) This is a result of the fact that the GGA exchange hole describes the exact exchange hole close to the reference electron more accurately than the LDA hole does The LDA hole is more diffuse, thus leading to an underestimation of exchange and stronger SIE effects, where the magnitude of the SIE energy is primarily due to the contribution of the core orbitals The GGA exchange hole is more compact, which leads to an exaggeration of exchange in the bond and the nonbonding region and negative SIE contributions Partitioning of the SIE into intra-/interelectronic and individual orbital contributions makes it possible to test the performance of a given exchange functional in different regions of the molecule It is shown that Hartree–Fock exchange always covers some long-range effects via interelectronic exchange while self-interaction-corrected DFT is lacking these effects

Long-distance electron tunneling in proteins

Abstract: Long-distance tunneling is the major mechanism of electron transfer (ET) in proteins. For a number of years, a major question has been whether specific electron tunneling pathways exist. This question is still debated in the literature, because the pathways are not observed directly, and interpretation of experimental results on ET rates involves ambiguities. The extremely small tunneling interactions are difficult to calculate accurately. Recently, there has been remarkable progress in the area; however, some problems still remain unresolved. The accurate prediction of the absolute rates of long-distance ET reactions and other biological charge-transfer reactions is a particularly pressing issue. The current theoretical calculations indicate that the specific paths do exist in static protein structures. However, the protein motions can result in significant averaging of the spatial tunneling patterns, and it is not clear how accurately subtle quantum interference effects are described by the present theories. The key to resolving these issues is to perform accurate, first-principles calculations of electron tunneling that include the dynamics of the protein. This paper reviews some of theoretical issues of electron tunneling dynamics in inhomogeneous organic media.

The role of vibronic interactions on intramolecular and intermolecular electron transfer in π-conjugated oligomers

Abstract: The importance of electron-vibrational coupling for intermolecular and intramolecular electron-transfer processes is discussed on the basis of first-principles correlated quantum-mechanical calculations and of a dynamic vibronic approach. The methodology is illustrated for examples selected from some of our recent work. In all instances, the theoretical results are thoroughly compared to experimental data.

The intermolecular interaction in the charge-transfer complexes between amines and halogens: A theoretical characterization of the trends in halogen bonding

Abstract: The trends in the properties of prereactive or charge-transfer complexes formed between the simple amines NH3, CH3NH2, (CH3)2NH, and (CH3)3N and the halogens F2, ClF, Cl2, BrF, BrCl, and Br2 were investigated by the ab initio restricted Hartree–Fock approach, the Moller–Plesset second-order method, and with several density functional theory variants using extended polarized basis sets. The most important structural parameters, the stabilization energies, the dipole moments, and other quantities characterizing the intermolecular halogen bond in these complexes are monitored, discussed, and compared. A wide range of interaction strengths is spanned in these series. Successive methyl substitution of the amine as well as increasing polarities and polarizabilities of the halogen molecules both systematically enhance the signature of charge-transfer interaction. These trends in halogen bonds of varying strength, in many aspects, parallel the features of hydrogen bonding.

Why are hexavalent uranium cyanides rare while U–F and U–O bonds are common and short?

Abstract: Relativistic small-core pseudopotential B3LYP and CCSD(T) calculations and frozen-core PW91–PW91 studies are reported for the series UF4X2 (X=H, F, Cl, CN, NC, NCO, OCN, NCS and SCN). The bonding in UF6 is analyzed and found to have some multiple-bond character, approaching at a theoretical limit a bond order of 1.5. In addition to these σ and π orbital interactions, the electrostatic attraction is important. Evidence for π bonding in the other systems studied was also found. The triatomic pseudohalides as well as fluorine and chlorine are in this sense better ligands than cyanide. The –CN group is a σ donor and π acceptor, as uranium itself, and hence is unfit to bond to U(VI). The σ-bonded UH6 is octahedral.

Atom-type description language: a universal language to recognize atom types implemented in the VEGA program

Abstract: The atom-type description language (ATDL) is a universal language used to describe and recognize the atom types from chemical connectivity. In this paper the ATDL approach specifications are reported with several examples. To date, this language is implemented in VEGA (http://www.ddl.unimi.it), a multipurpose program able to convert and manage several molecular file formats. This software uses the ATDL to assign the correct atom types in order to help several functions (file format conversion, molecular properties calculation, surface mapping and interaction energy analysis).

Simulating quantum dynamics in classical environments

Abstract: Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum–classical systems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approximation. The dynamics of these composite systems are governed by a quantum–classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of trajectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many-body environments.

Transition states from empirical force fields

Abstract: This is an overview of the use of empirical force fields in the study of reaction mechanisms. Empirical-valence-bond-type methods (including reactive force field and multiconfigurational molecular mechanics) produce full reaction surfaces by mixing, in the simplest case, known force fields describing reactants and products. The SEAM method instead locates approximate transition structures by energy minimization along the intersection of the component force fields. The transition-state force-field approach (including Q2MM) designs a new force field mimicking the transition structure as an energy minimum. The scope and applicability of the various methods are compared.

Towards a ‘‘next generation’’ neglect of diatomic differential overlap based semiempirical molecular orbital technique

Abstract: We discuss problems and features of current semiempirical molecular orbital techniques and test some of the approximations and assumptions used. Prerequisites for a ‘‘next generation’’ technique include orthogonalization corrections, effective core potentials and an implicit dispersion term. However, validation of experimental parameterization data using density functional theory or the Gaussian 2 approach reveals significant errors in some cases. Developers of future methods will need to validate all their parameterization data and may no longer be able to parameterize for heats of formation at 298 K, but may need to use Born–Oppenheimer binding energies. We also suggest that there is no inherent reason that semiempirical techniques should not reproduce hydrogen bonding and show that the Gaussian potentials added to the core–core terms in AM1 and the PMn methods actually weaken hydrogen bonding, rather than strengthening it.

Two-electron distribution functions and intracules

Abstract: Two-electron distribution functions and intracules are functions of electronic coordinates and occupy an important, and frequently overlooked, middle ground between the beguiling simplicity of electron densities and the bewildering complexity of wavefunctions. We survey the functions that have been considered by earlier workers and introduce two new ones, the Wigner intracule and the action intracule, that have not previously been discussed. To illustrate their usefulness, we consider the intracules of jellium, a few small atoms and the dissociating hydrogen molecule.

Correlating basis sets for the H atom and the alkali-metal atoms from Li to Rb

Abstract: Contracted Gaussian-type function sets are developed for correlating p, d, and f functions for a valence electron of the hydrogen atom and alkali-metal atoms from Li to Rb. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from the K orbitals of the atoms. The present basis sets yield an accuracy comparable to the correlation-consistent basis set for the hydrogen atom and also give a similar high accuracy for the alkali-metal atoms. In the calculations of spectroscopic constants of alkali hydrides, the decontraction of the p function plays an important role, especially for LiH. The contributions of d and f functions are nontrivial for KH and RbH.

Mechanism and control of molecular energy flow: a modeling perspective

Abstract: Vibrational energy flow in organic molecules occurs by a multiple-time-scale mechanism that can be modeled by a single exponential only in its initial stages. The mechanism is a consequence of the hierarchical structure of the vibrational Hamiltonian, which leads to diffusion of vibrational wavepackets on a manifold with far fewer than the 3N−6 dimensions of the full vibrational state space. The dynamics are controlled by a local density of states, which does not keep increasing with molecular size. In addition, the number of vibrational coordinates severely perturbed during chemical reaction is small, leading to preservation of the hierarchical structure at chemically interesting energies. This regularity opens up the possibility of controlling chemical reactions by controlling the vibrational energy flow. Computationally, laser control of intramolecular vibrational energy redistribution can be modeled by quantum-classical, or by purely quantum-mechanical models of the molecule and control field.

Electronic coupling in electron transfer and the influence of nuclear modes: theoretical and computational probes

Abstract: Long-range electronic coupling of local donor and acceptor sites is formulated in the context of thermal and optical electron transfer and then illustrated with examples based on electronic structure calculations. The relationship of the calculated results to available experimental kinetic and optical data is discussed in detail. The influence of nuclear modes on the magnitude of the coupling (i.e., departures from the Condon approximation) is investigated in terms of both discrete molecular modes and solvent modes, and a general expression is presented for the modulation of the superexchange tunneling gap by motion along the electron transfer reaction coordinate.

Cesium and barium as honorary d elements: CsN7Ba as an example

Abstract: Quantum chemical calculations suggest that inverse sandwich compounds with the general formula MN7M′, where M is an alkali metal (K,Rb,Cs), N7 is a ten-π-electron ring, and M′ is an alkaline-earth metal (Ca,Sr,Ba), are local C7v minima Among these systems, the CsN7Ba molecule is the stablest of all and presents a barrier of 35 kcal/mol to dissociation towards CsNBa and three N2 molecules Substantial 5d character is found in the bonding Possible ways of making these high-energy compounds are discussed

Parameterization of semiempirical methods to treat nucleophilic attacks to biological phosphates: AM1/d parameters for phosphorus

Abstract: This paper reports a new AM1/d model for phosphorus that can be used to model nucleophilic attack of phosphates relevant for biological phosphate hydrolysis reactions. The parameters were derived from a quantum dataset calculated with hybrid density-functional theory [B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)] of phosphates and phosphoranes in various charge states, and on transitions states for nucleophilic attacks. A suite of non-linear optimization methods is outlined for semiempirical parameter development based on integrated evolutionary (genetic), Monte Carlo simulated annealing and direction set minimization algorithms. The performance of the new AM1/d model and the standard AM1 and MNDO/d models are compared with the density-functional results. The results demonstrate that the strategy of developing semiempirical parameters specific for biological reactions offers considerable promise for application to large-scale biological problems.

The performance of density functional theory for LnF (Ln=Nd, Eu, Gd, Yb) and YbH

Abstract: Different density functional theory (DFT) functionals have been evaluated by studying geometries and bond strengths of YbH, YbF, EuF, GdF, and NdF and compared with accurate CCSD(T) results and, when available, experiment. The agreement between the CCSD(T) results and experiment, when available, is good. The agreement is also good between bond strengths calculated at the DFT level using relativistic effective core potentials and the CCSD(T) results. However, the all-electron ADF calculations systematically overestimate binding energies. The geometries obtained by both the all-electron and the effective-core-potential-based DFT calculations are generally in good agreement with the CCSD(T) results.

A charge-scaling method to treat solvent in QM/MM simulations

Abstract: We present a method to treat the solvent efficiently in hybrid quantum mechanical/molecular mechanical simulations of chemical reactions in enzymes. The method is an adaptation of an approach developed for molecular-mechanical free-energy simulations. The charges of each of the exposed ionizable groups are scaled, and the system is simulated in the presence of a limited number of explicit solvent molecules to obtain a reasonable set of structures. Continuum electrostatics methods are then used to correct the energies. Variations in the procedure are discussed with an emphasis on modifications from the original protocol. We illustrate the method by applying it to the study of a hydrolysis reaction in a highly charged system comprising a complex between the base excision repair enzyme uracil-DNA glycosylase and double-stranded DNA. The resulting adiabatic reaction profile is in good agreement with experiment, in contrast to that obtained without scaling the charges.

A valence-bond-based complete-active-space self-consistent-field method for the evaluation of bonding in organic molecules

Abstract: We present the complete-active-space self-consistent-field (CASSCF) implementation of a valence-bond (VB) based method for the analysis of bonding in organic molecules. The method uses the spin-exchange density matrix P with a localized orbital basis, where the determinants of the CASSCF wavefunction become VB-like determinants with different spin coupling patterns. The index P ij evaluates the contributions of the determinants to the CASSCF wavefunction and is used to generate resonance formulas. We use the bonding contributions in the original VB formulation of the method (αβ terms). The method is applied in studies of excited-state reactivity, as shown here for indole. Its first excited state is covalent and is characterized by a decrease in the bond orders in the benzene moiety, similar to the B 2u excited state of benzene. In contrast, the ionic excited state has an inversion in the bonds of the pyrrole moiety induced by charge transfer to the benzene ring.

Modeling water exchange on monomeric and dimeric Mn centers

Abstract: Water exchange on Mn centers in proteins has been modeled with density functional theory using the B3LYP functional. The reaction barrier for dissociative water exchange on [MnIV(H2O)2(OH)4] is only 9.6 kcal mol−1, corresponding to a rate of 6×105 s−1. It has also been investigated how modifications of the model complex change the exchange rate. Three cases of water exchange on Mn dimers have been modeled. The reaction barrier for dissociative exchange of a terminal water ligand on [(H2O)2(OH)2MnIV(μ-O)2MnIV(H2O)2(OH)2] is 8.6 kcal mol−1, while the bridging oxo group exchange with a ring-opening mechanism has a barrier of 19.2 kcal mol−1. These results are intended for interpretations of measurements of water exchange for the oxygen evolving complex of photosystem II. Finally, a tautomerization mechanism for exchange of a terminal oxyl radical has been modeled for the synthetic O2 catalyst [(terpy)(H2O)MnIV(μ-O)2MnIV(O•)(terpy)]3+ (terpy=2,2′:6,2″-terpyridine). The calculated reaction barrier is 14.7 kcal mol−1.

NMR chemical shifts in the low–pH form of a-chymotrypsin. A QM/MM and ONIOM–NMR study

Abstract: The relationship between hydrogen bonding and NMR chemical shifts in the catalytic triad of low-pH α-chymotrypsin is investigated by combined use of the effective fragment potential [(2001) J Phys Chem A 105:293] and ONIOM–NMR [(2000) Chem Phys Lett 317:589] methods. Our study shows that while the His57 Nδ1−H bond is stretched by a relatively modest amount (to about 1.060 A) this lengthening, combined with the polarization due to the molecular environment, is sufficient to explain the experimentally observed chemical shifts of 18.2 ppm. Furthermore, the unusual down-field shift of Hɛ1 (9.2 ppm) observed experimentally is reproduced and shown to be induced by interactions with the C=O group of Ser214 as previously postulated. The free-energy cost of moving Hδ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol.

Valence ab initio calculation of the potential-energy curves for the Ca2 dimer

Abstract: The electronic structure of the Ca2 molecule has been investigated by use of a two-valence-electron semiempirical pseudopotential and applying the internally contracted multireference configuration interaction method with complete-active-space self-consistent-field reference wave functions. Core–valence correlation effects have been accounted for by adding a core-polarization potential to the Hamiltonian. The ground-state properties of the Ca2 and Ca2 + dimers have also been studied at the single-reference coupled-cluster level with single and double excitations including a perturbative treatment of triple excitations. Good agreement with experiment has been obtained for the ground-state potential curve and the only experimentally known A1Σ u + excited state of Ca2. The spectroscopic parameters D e and R e deduced from the calculated potential curves for other states are also reported. In addition, spin–orbit coupling between the singlet and triplet molecular states correlating, respectively, with the (4p)1P and (4p)3P Ca terms has been investigated using a semi-empirical two-electron spin–orbit pseudopotential.