Comprehensive relativistic ab initio and density functional theory studies on PtH, PtF, PtCl, and Pt(NH(3))(2)Cl(2)

Platinum monohydride is taken as an example to compare the performance of various relativistic and correlation approaches, such as all-electron DPT (direct perturbation theory), ECP (effective core potential); RSPT2, RSPT3 (second- and third-order multireference Rayleigh-Schr?dinger perturbation theory), CCSD(T) (coupled-cluster with singles, doubles, and perturbative triples), as well as the four-component relativistic density functional theory. It is shown that first-order DPT performs significantly better than the (first-order) Breit-Pauli Hamiltonian. The performance of different approaches for the excitation energies of the platinum diatomics is discussed critically. The molecular spectroscopic constants for PtF and PtCl are predicted for the first time. The geometric data for several isomers of cis- and trans-Pt(NH(3))(2)Cl(2) are reported. The corresponding energetic data are calculated at relativistic all-electron and ECP-CCSD(T) as well as four-component relativistic density functional levels of theory. Contrary to previous results, it is found that the two C(2v) isomers of cis-Pt(NH(3))(2)Cl(2) are marginally separated in energy, which could be ascribed to Cl-H interactions.     

Accuracy and limitations of second-order many-body perturbation theory for predicting vertical detachment energies of solvated-electron clusters

Vertical electron detachment energies (VDEs) are calculated for a variety of (H(2)O)(n)(-) and (HF)(n)(-) isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order M?ller-Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H(2)O)(n)(-) clusters (n< or = 7), the correlation energy associated with the unpaired electron grows linearly as a function of the VDE but is unrelated to the number of monomers, n. In every example considered here, including strongly-bound "cavity" isomers of (H(2)O)(24)(-), the correlation energy associated with the unpaired electron is significantly smaller than that associated with typical valence electrons. As a result, the error in the MP2 detachment energy, as a fraction of the CCSD(T) value, approaches a limit of about -7% for (H(2)O)(n)(-) clusters with VDEs larger than about 0.4 eV. CCSD(T) detachment energies are bounded from below by MP2 values and from above by VDEs calculated using second-order many-body perturbation theory with molecular orbitals obtained from density functional theory. For a variety of both strongly- and weakly-bound isomers of (H(2)O)(20)(-) and (H(2)O)(24)(-), including both surface states and cavity states, these bounds afford typical error bars of +/-0.1 eV. We have found only one case where the Hartree-Fock and density functional orbitals differ qualitatively; in this case the aforementioned bounds lie 0.4 eV apart, and second-order perturbation theory may not be reliable.     

Evaluation of theoretical approaches for describing the interaction of water with linear acenes

The interaction of a water monomer with a series of linear acenes (benzene, anthracene, pentacene, heptacene, and nonacene) is investigated using a wide range of electronic structure methods, including several "dispersion"-corrected density functional theory (DFT) methods, several variants of the random phase approximation (RPA), DFT-based symmetry-adapted perturbation theory with density fitting (DF-DFT-SAPT), MP2, and coupled-cluster methods. The DF-DFT-SAPT calculations are used to monitor the evolution of the electrostatics, exchange-repulsion, induction, and dispersion contributions to the interaction energies with increasing acene size and also provide the benchmark data against which the other methods are assessed.     

High-order electron-correlation methods with scalar relativistic and spin-orbit corrections

An assortment of computer-generated, parallel-executable programs of ab initio electron-correlation methods has been fitted with the ability to use relativistic reference wave functions. This has been done on the basis of scalar relativistic and spin-orbit effective potentials and by allowing the computer-generated programs to handle complex-valued, spinless orbitals determined by these potentials. The electron-correlation methods that benefit from this extension are high-order coupled-cluster methods (up to quadruple excitation operators) for closed- and open-shell species, coupled-cluster methods for excited and ionized states (up to quadruples), second-order perturbation corrections to coupled-cluster methods (up to triples), high-order perturbation corrections to configuration-interaction singles, and active-space (multireference) coupled-cluster methods for the ground, excited, and ionized states (up to active-space quadruples). A subset of these methods is used jointly such that the dynamical correlation energies and scalar relativistic effects are computed by a lower-order electron-correlation method with more extensive basis sets and all-electron relativistic treatment, whereas the nondynamical correlation energies and spin-orbit effects are treated by a higher-order electron-correlation method with smaller basis sets and relativistic effective potentials. The authors demonstrate the utility and efficiency of this composite scheme in chemical simulation wherein the consideration of spin-orbit effects is essential: ionization energies of rare gases, spectroscopic constants of protonated rare gases, and photoelectron spectra of hydrogen halides.     

Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using M?ller-Plesset-type (MP) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational implementation of the latter is based on a Neumann series which, interestingly, even though the effect is small, usually diverges. A convergence technique, which perhaps can be applied in other uses of Neumann series in perturbation theory, is proposed. The numerical results thus obtained show that, in weakly bound systems, self-consistency can be neglected since the long-range correlation does not affect the density significantly. Although MP is not adequate for multireference systems, it can still be used as a reliable analysis tool. Though the density change is not negligible anymore in such cases, self-consistency effects are found to be much smaller than long-range correlation effects (less than 10% for the systems considered). For that reason, a sensible approximation might be to update the short-range energy functional term while freezing its functional derivative, namely, the short-range local potential, in the wave function optimization. The accuracy of such an approximation still needs to be assessed.     

Quantum chemical design of hydroxyurea derivatives for the treatment of sickle-cell anemia

Treatment of sickle-cell anemia by hydroxyurea has been shown to decrease patient mortality by 40%. In a rate-limiting step, hydroxyurea reacts with hemoglobin to form the nitroxide radical, which then decomposes to yield nitric oxide (NO). In this paper, we examine derivatives of hydroxyurea and their radicals by quantum chemical methods to identify derivatives that generate NO-producing radicals at a faster rate than hydroxyurea. The molecules are treated with Hartree-Fock theory, correlated wave function methods such as perturbation theory and coupled-cluster methods, and density functional theory. We observe that the inclusion of the correlation energy is important for an accurate comparison of the energy changes associated with modifications of the hydroxyurea molecule and its radical. The computational results are compared with available experimental data. All 19 derivatives of hydroxyurea, including a new medication for asthma Zileuton, manifest changes in their electronic energies that mark them as candidates for a faster formation of NO-producing radicals.     

Ab initio density functional theory applied to quasidegenerate problems

Ab initio density functional theory (DFT), previously applied primarily at the second-order many-body perturbation theory (MBPT) level, is generalized to selected infinite-order effects by using a new coupled-cluster perturbation theory (CCPT). This is accomplished by redefining the unperturbed Hamiltonian in ab initio DFT to correspond to the CCPT2 orbital dependent functional. These methods are applied to the Be-isoelectronic systems as an example of a quasidegenerate system. The CCPT2 variant shows better convergence to the exact quantum Monte Carlo correlation potential for Be than any prior attempt. When using MBPT2, the semicanonical choice of unperturbed Hamiltonian, plays a critical role in determining the quality of the obtained correlation potentials and obtaining convergence, while the usual Kohn-Sham choice invariably diverges. However, without the additional infinite-order effects, introduced by CCPT2, the final potentials and energies are not sufficiently accurate. The issue of the effects of the single excitations on the divergence in ordinary OEP2 is addressed, and it is shown that, whereas their individual values are small, their infinite-order summation is essential to the good convergence of ab initio DFT.     

Coupled-cluster singles and doubles for extended systems

Coupled-cluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupled-cluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second- and third-order many-body perturbation theories, are formulated and implemented for infinitely extended one-dimensional systems (polymers), on the basis of the periodic boundary conditions and distance-based screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short- and long-range lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of pi-electron conjugation or the fundamental band gaps. The t2 and t1 amplitudes in the atomic orbital (AO) basis are obtained by first computing the t amplitudes in the Bloch-orbital basis and subsequently back-transforming them into the AO basis. The plot of these AO-based t amplitudes as a function of unit cells also indicates that the t2 amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably 1/r3. The AO-based t1 amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below 10(-6) hartree after 15 A for all three polymers. The basis set dependence of the decay behavior of t2 amplitudes is also examined for linear hydrogen fluoride polymer (HF)infinity and linear beryllium polymer (Be)infinity employing the STO-3G, 6-31G, and 6-31G* basis sets, and proves to be rather small.     

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.     

Importance of structural motifs in liquid hydrogen fluoride

The investigation of liquid phases by means of accurate electronic structure methods is a demanding task due to the high computational effort. We applied second-order M?ller-Plesset perturbation theory and high-level quantum chemical calculations using the coupled-cluster method with single, double and perturbative triple excitations in combination with Dunnings correlation-consistent basis sets up to quintuple ζ quality. Based on these calculations, we extrapolated the correlation energy to the basis set limit in order to improve the results even further. For comparison to the correlated electronic structure methods, density functional calculations employing different functionals are presented as well. The investigated species are a cyclic pentamer as well as a set of branched structures. The quantum cluster equilibrium method is employed for the investigation of the liquid-phase structure of hydrogen fluoride. The pentamer is found to be present to a high extent and in the case of the MP2/QZVP data, its presence improves the results significantly. Accounting for branched structures slightly improves results, so that they are found to be present but not to dominate in liquid hydrogen fluoride. Concerning both the interaction energy and the result of the quantum cluster equilibrium calculation the basis set has a major influence, whereas the difference between M?ller-Plesset perturbation theory and coupled-cluster calculations is less pronounced.     

The exchange-correlation potential in ab initio density functional theory

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.     

Quantum Monte Carlo study of the ground state and low-lying excited states of the scandium dimer

A large set of electronic states of scandium dimer has been calculated using high-level theoretical methods such as quantum diffusion Monte Carlo (DMC), complete active space perturbation theory as implemented in GAMESS-US, coupled-cluster singles, doubles, and triples, and density functional theory (DFT). The 3 Sigma u and 5 Sigma u states are calculated to be close in energy in all cases, but whereas DFT predicts the 5 Sigma u state to be the ground state by 0.08 eV, DMC and CASPT2 calculations predict the 3 Sigma u to be more stable by 0.17 and 0.16 eV, respectively. The experimental data available are in agreement with the calculated frequencies and dissociation energies of both states, and therefore we conclude that the correct ground state of scandium dimer is the 3 Sigma u state, which breaks with the assumption of a 5 Sigma u ground state for scandium dimer, believed throughout the past decades.     

Thermochemistry of key soot formation intermediates: C3H3 isomers

Accurate standard enthalpies of formation for allene, propyne, and four C3H3 isomers involved in soot formation mechanisms have been determined through systematic focal point extrapolations of ab initio energies. Auxiliary corrections have been applied for anharmonic zero-point vibrational energy, core electron correlation, the diagonal Born-Oppenheimer correction (DBOC), and scalar relativistic effects. Electron correlation has been accounted for via second-order Z-averaged perturbation theory (ZAPT2) and primarily through coupled-cluster theory, including single, double, and triple excitations, as well as a perturbative treatment of connected quadruple excitations [ROCCSD, ROCCSD(T), ROCCSDT, and UCCSDT(Q)]. The correlation-consistent hierarchy of basis sets, cc-pVXZ (X = D, T, Q, 5, 6), was employed. The CCSDT(Q) corrections do not exceed 0.12 kcal mol(-)1 for the relative energies of the systems considered here, indicating a high degree of electron correlation convergence in the present results. Our recommended values for the enthalpies of formation are as follows: Delta(f)H(o)(0)(propargyl) = 84.76, Delta(f)H(o)(0) (1-propynyl) = 126.60, Delta(f)H(o)(0) (cycloprop-1-enyl) = 126.28, Delta(f)H(o)(0)(cycloprop-2-enyl) = 117.36, Delta(f)H(o)(0)(allene) = 47.41, and Delta(f)H(o)(0)(propyne) = 46.33 kcal mol(-1), with estimated errors no larger than 0.3 kcal mol(-1). The corresponding C3H3 isomerization energies are about 1 kcal mol(-1) larger than previous coupled-cluster results and several kcal mol(-1) below those previously obtained using density functional theory.     

Ab initio many-body investigation of structure and stability of two-fold rings in silicates

In this paper we present ab initio many-body calculations on the strain energy of W silica, taken as a model system for edge-sharing tetrahedral SiO(2) systems with respect to corner-sharing ones as in alpha quartz. The mean-field results were obtained using the restricted Hartree-Fock approach, while the many-body effects were taken into account by the second-order M?ller-Plesset perturbation theory and the coupled-cluster approach. Correlation contributions are found to play an important role to determine the stability of edge-sharing units. The most sophisticated method used in our calculation, i.e., the coupled-cluster approach with single and double excitations, yields a strain energy of 0.0427 a.u. per Si(2)O(4) unit with respect to alpha quartz, which is even smaller than the value obtained by a previous density functional theory calculation.     

PRIRODA-04: a quantum-chemical program suite. New possibilities in the study of molecular systems with the application of parallel computing

Main characteristics are described of the PRIRODA quantum-chemical program suite designed for the study of complex molecular systems by the density functional theory, at the MP2, MP3, and MP4 levels of multiparticle perturbation theory, and by the coupled-cluster single and double excitations method (CCSD) with the application of parallel computing. A number of examples of calculations are presented.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 804–810, March, 2005.     

Comparative density functional theory and post-Hartree-Fock (CCSD, CASSCF) studies on the electronic structure of halogen nitrites ClONO and BrONO using quantum chemical topology

In this paper, the electronic structures of cis- and trans-ClONO and BrONO are studied at the CCSD∕aug-cc-pVTZ, CASSCF(14,12)/aug-cc-pVTZ, and B3LYP/aug-cc-pVTZ computational levels. For the Cl-O bond, topological analysis of the electron density field, ρ(r), shows the prevalence of the shared-electron type bond (?(2)ρ((3,-1)) < 0). The Br-O bond, however, represents the closed-shell interaction (?(2)ρ((3,-1)) > 0). Topological analysis of the electron localization function, η(r), and electron localizability indicator (ELI-D), (D) (σ)(r), shows that the electronic structure of the central N-O bond is very sensitive to both electron correlation improvements (coupled-cluster single double (CCSD), CASSCF, density functional theory (DFT)) and bond length alteration. Depending on the method used, the N-O bond can be characterized as a "normal" N-O bond with a disynaptic V(N,O) basin (DFT); a protocovalent N-O bond with two monosynaptic, V(N) and V(O), basins (CCSD, CASSCF); or a new type, first discovered for FONO, characterized by a single monosynaptic, V(N) basin (CCSD, DFT). The total basin population oscillates between 0.46-0.96 e (CCSD) and 0.86-1.02 e (CASSCF). The X-O bond is described by the single disynaptic basin, V(X,O), with a basin population between 0.76 and 0.81 e (CCSD) or 0.77 and 0.85 e (CASSCF). Analysis of the localized electron detector distribution for the cis-Cl-O1-N=O2 shows a manifold in the Cl···O2 region, associated with decreased electron density.     

Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i) A linearized scheme of the quadratic equation used to determine the cluster amplitudes. ii) The effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods.