Large-scale Coupled Cluster Calculations Research Articles

Extreme Correlation Effects in the Elusive Bound Spectrum of C60–

We report on large-scale coupled cluster calculations of the electron affinities of the C60 fullerene. The full spectrum of bound states of the anion is investigated. Thereby, a new state bound by correlation is discovered. The binding of this state is highly dependent on the correct description of the polarization and the electron correlation in the fullerene. We present the natural orbital occupied by the excess electron for each of the anionic states and show how the bound spectrum can be divided into two different groups according to their binding mechanism. We discuss in depth how approximating the correlation with perturbation theory leads in the case of the C60– anion to unreliable predictions of the electron affinities in contrast to other large clusters and molecules. Some possible implications of the new weakly bound state are discussed.

Towards highly accurate ab initio thermochemistry of larger systems: Benzene

The high accuracy extrapolated ab initio thermochemistry (HEAT) protocol is applied to compute the total atomization energy (TAE) and the heat of formation of benzene. Large-scale coupled-cluster calculations with more than 1500 basis functions and 42 correlated electrons as well as zero-point energies based on full cubic and (semi)diagonal quartic force fields obtained with the coupled-cluster singles and doubles with perturbative treatment of the triples method and atomic natural orbital (ANO) triple- and quadruple-zeta basis sets are presented. The performance of modifications to the HEAT scheme and the scaling properties of its contributions with respect to the system size are investigated. A purely quantum-chemical TAE and associated conservative error bar of 5463.0 ± 3.1 kJ mol(-1) are obtained, while the corresponding 95% confidence interval, based on a statistical analysis of HEAT results for other and related molecules, is ± 1.8 kJ mol(-1). The heat of formation of benzene is determined to be 101.5 ± 2.0 kJ mol(-1) and 83.9 ± 2.1 kJ mol(-1) at 0 K and 298.15 K, respectively.

Coupled-cluster calculations of C2H2Si and CNHSi structural isomers

Results of large-scale coupled-cluster calculations of selected C(2)H(2)Si and CNHSi structural isomers are reported. Equilibrium molecular structures of a total of 12 molecules in their singlet electronic states have been calculated systematically employing the coupled-cluster singles and doubles model augmented by a perturbative correction for triple excitations (CCSD(T)) in combination with Dunning's hierarchy of correlation consistent basis sets. In addition, anharmonic force fields were calculated to yield fundamental vibrational frequencies and rotation-vibration interaction constants alpha(i) (A,B,C). The latter were used to determine empirical equilibrium structures r(e) (emp) of two molecules - silacyclopropenylidene, c-C(2)H(2)Si, and silapropadienylidene, H(2)CCSi - for which sufficient isotopic data are available from literature. Very good agreement with theoretical equilibrium structures from CCSD(T) calculations employing core-valence basis sets of quadruple and quintuple-zeta quality - i.e., cc-pwCVQZ (337 basis functions), cc-pCV5Z, and cc-pwCV5Z (581 basis functions) is found - to within 0.001 A for bond lengths and 0.1 degrees for bond angles. Theoretical ground state rotational constants of HSiCN and HSiNC compare very favorably with experimental microwave data from literature, to within 0.15% (HSiCN) and 0.1% (HSiNC) for the B(0) and C(0) rotational constants. In the case of c-C(2)H(2)Si and H(2)CCSi this agreement is even better than 0.1%. For the latter two molecules effects of higher-level electron-correlation and relativity to the equilibrium geometry as well as the electronic contributions to the rotational constants are investigated. For eight molecules not yet studied at high spectral resolution in the gas-phase theoretical molecular parameters are provided to support future laboratory investigations. Theoretical vibrational fundamentals compare well with data of eight species studied previously with infrared matrix isolation spectroscopy.

Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives.

In this paper we present a parallel adaptation of a highly efficient coupled-cluster algorithm for calculating coupled-cluster singles and doubles (CCSD) and coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations (CCSD(T)) energies, gradients, and, for the first time, analytic second derivatives. A minimal-effort strategy is outlined that leads to an amplitude-replicated, communication-minimized implementation by parallelizing the time-determining steps for CCSD and CCSD(T). The resulting algorithm is aimed at affordable cluster architectures consisting of compute nodes with sufficient memory and local disk space and that are connected by standard communication networks like Gigabit Ethernet. While this scheme has disadvantages in the limit of very large numbers of compute nodes, it proves to be an efficient way of reducing the overall computational time for large-scale coupled-cluster calculations. In this way, CCSD(T) calculations of molecular properties such as vibrational frequencies or NMR-chemical shifts for systems with more than 1000 basis functions are feasible. A thorough analysis of the time-determining steps for CCSD and CCSD(T) energies, gradients, and second derivatives is carried out. Benchmark calculations are presented, proving that the parallelization of these steps is sufficient to obtain an efficient parallel scheme. This also includes the calculation of parallel CCSD energies and gradients using unrestricted (UHF) and restricted open-shell (ROHF) Hartree-Fock references, parallel UHF-CCSD(T) energies and gradients, parallel ROHF-CCSD(T) energies as well as parallel equation-of-motion CCSD energies and gradients for closed- and open-shell references. First applications to the calculation of the NMR chemical shifts of benzene using large basis sets and to the calculation of the equilibrium geometry of ferrocene as well as energy calculations with more than 1300 basis functions demonstrate the efficiency of the implementation.

The proton-bound complex Cl −⋯H-CCl 3: A high-level theoretical study

Large-scale coupled cluster calculations within variant CCSD(T) have been employed to study major portions of the potential energy and electric dipole moment surfaces for the hydrogen-bonded anionic complex Cl −⋯H-CCl 3. The recommended dissociation energy D 0 is 6280 cm −1 or 75.1 kJ mol −1, with an estimated error of ca. 1%. Upon complex formation, the weak CH stretching vibration ( ν 1) of free HCCl 3 experiences an intensity enhancement by four orders of magnitude, with anharmonicity effects playing an important role. The band origins of the ν 1 bands of 35Cl −⋯H-C 35Cl 3 and 35Cl −⋯H-D 35Cl 3 are calculated at 2553 and 1949 cm −1, respectively.

Relativistic effective core potential calculations of Hg and eka-Hg (E112) interactions with gold: Spin-orbit density functional theory modeling of Hg–Aun and E112–Aun systems

Interactions of eka-Hg (E112) and Hg atoms with small gold clusters were studied in the frame of the relativistic effective core potential model using the density functional theory (DFT) approach incorporating spin-dependent (magnetic) interactions. The choice of the exchange-correlation functional was based on a comparison of the results of DFT and large-scale coupled cluster calculations for E112Au and HgAu at the scalar relativistic level. A close similarity between the E112Aun and HgAun equilibrium structures was observed. The E112 binding energies on Aun are typically smaller than those for Hg by ca. 25%-32% and the equilibrium E112-Au separations are always slightly larger than their Hg-Au counterparts.

On the equilibrium structures and the IR active bending vibrations of linear C13 and C15: results of large-scale coupled cluster calculations

Accurate equilibrium (re) structures (ca. 0.0005 A accuracy in bond lengths) have been established for linear C13 and C15 by applying a uniform correction to the results of CCSD(T) calculations with the cc-pVQZ basis set. The equilibrium bond lengths cover a small range between 1.2690 and 1.2928 A and are indicative of strong carbon–carbon double bonds. Equilibrium structures of still longer chains may be obtained by taking the recommended re structure for C15 and inserting one or more C2 links with Re = 1.277 A in the middle of the molecule. Both linear C13 and C15 exhibit no sign of floppiness and appear to behave like fairly normal semi-rigid molecules. Diagonal potentials for the IR active bending vibrations of both molecules have large correlation contributions between -33 and 47%, with MP2 strongly overshooting with respect to CCSD(T). Harmonic cis-bending vibrational wavenumbers and their absolute IR intensities are predicted. Since the latter are rather small, the chances of an interstellar detection of linear C13 or C15 in the far IR may be poor.

Low-energy electron scattering ofNO:Ab initioanalysis of theΣ−3,Δ1, andΣ+1shape resonances in the local complex potential model

We present an ab initio study of elastic scattering and vibrational excitation of $\mathrm{NO}$ by low-energy $(0--2.0\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ electron impact. The low-energy scattering cross sections are dominated by shape resonance contributions associated with the $^{3}\ensuremath{\Sigma}^{\ensuremath{-}}$, $^{1}\ensuremath{\Delta}$, and $^{1}\ensuremath{\Sigma}^{+}$ states of ${\mathrm{NO}}^{\ensuremath{-}}$. Resonance parameters for the three anion states were extracted from an analysis of fixed-nuclei variational (complex Kohn) calculations that employed elaborate trial wave functions. Independent estimates of the resonance parameters were obtained by analytically continuing the results of large-scale coupled-cluster calculations into the plane of complex momentum. The local complex potential model was used to calculate vibrational excitation cross sections, as well as the resonant portion of the vibrationally elastic cross sections. These results were combined with background contributions from the fixed-nuclei calculations to compute elastic and grand total cross sections. Our results capture the essential features of recent measurements of the cross sections, but suggest the need at lower energies for a more sophisticated, nonlocal treatment of nuclear dynamics.

The Ar–HCCCN van der Waals complex: Microwave spectroscopy and coupled cluster calculations

Large-scale coupled cluster calculations have yielded an almost T-shaped equilibrium structure for the Ar–HCCCN van der Waals complex, with an equilibrium dissociation energy of De=221 cm−1. The theoretical predictions are confirmed by pulsed-nozzle Fourier transform microwave spectroscopy in the frequency range from 3 to 26 GHz. Strong b-type and much weaker a-type transitions have been observed, and the N14 nuclear quadrupole hyperfine components of the rotational transitions have been resolved. The spectral analysis has produced rotational, centrifugal distortion, and N14 nuclear quadrupole coupling constants. Structural parameters describing a (vibrationally averaged) T-shaped complex geometry have been derived.

Complexes of an argon atom with the linear anions HCC − and HC 4−: results of coupled cluster calculations

Large-scale coupled cluster calculations have been carried out for the complexes of an argon atom with the linear anions HCC − and HC 4 −. In both cases, almost T-shaped structures are energetically favoured. Their equilibrium dissociation energies ( D e) are predicted to be 501(5) and 507(5) cm −1, respectively. In contrast to the isoelectronic neutral systems Ar + HCN and Ar + HC 3N, no energy minima are found for the ‘hydrogen-bonded’ configurations. While the complex Ar ⋯ HCC − is rather flexible, Ar ⋯ HC 4 − appears to be fairly rigid, quite similar to isoelectronic Ar ⋯ HC 3N or Ar ⋯ HC 4H.

Complexes of an argon atom with linear cations: results of coupled cluster calculations

Large-scale coupled cluster calculations have been carried out for complexes between an argon atom and four different linear cations (HCNH +, HC 3NH +, HCCH +, and HC 4H +). The two former closed-shell species have hydrogen-bonded linear forms, with nitrogen acting as proton donor, as the energetically most stable isomers. Their dissociation energies ( D 0) are predicted to be 1261 and 1051 cm −1 , respectively. For Ar⋯HCCH +, the T-form with 2A 1 symmetry is the absolute energy minimum of the potential energy surface, lying 1228 cm −1 below the fragments at infinite separation. Ar⋯HC 4H + has a dissociation energy less than half as large and slightly prefers the linear structure. Various spectroscopic properties are predicted for the closed-shell complexes under investigation.

Spectroscopic properties of interstellar molecules: Theory and experiment

Over the past two decades, the identification and characterisation of interstellar molecules has often benefitted from a fruitful interplay between theoretical chemistry, laboratory spectroscopy and (radio) astronomy. The article reports on various examples of this sort, concentrating on carbon chains which represent the most prominent structural motif among currently known interstellar molecules. Results of large-scale coupled cluster calculations are reported for cyanopolyynes (HC2n+1N) up to n = 5, the corresponding radicals C2n+1N, linear silicon carbides (SiCn), carbon–sulfur and pure carbon chains. Throughout, detailed comparison with experimental data is made wherever possible.

The anionic complex Cl−⋯ HCCH: Results of large-scale coupled cluster calculations

On the basis of large-scale coupled-cluster calculations the dissociation energy of the complex Cl−⋯ HCCH is predicted to be D0=3600 cm−1, with an uncertainty of the order of 1%. The ground state rotational constant is obtained to be 2053 (10) MHz and the wave number of the hydrogen-bonded CH stretching vibration is 2877±10 cm−1. Anharmonicity constants for the stretching vibrations are discussed in comparison with those calculated earlier for Br−⋯ HCCH and I−⋯ HCCH [P. Botschwina and H. Stoll, Phys. Chem. Chem. Phys. 3, 1965 (2001)].

Coupled cluster calculations for Ar⋯HCO+

Large-scale coupled cluster calculations involving connected triple substitutions were carried out for Ar⋯HCO+. The equilibrium structure of this complex is linear with Re(Ar⋯H)=2.126Å,r1e(CH)=1.109Å and r2e(CO)=1.107Å. The dissociation energy is predicted to be D0=1531cm−1, with an uncertainty of ca. 1%. Various spectroscopic properties (vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants and transition dipole moments) are predicted for Ar⋯HCO+ and Ar⋯DCO+.

The hydrogen-bonded cluster anions Br-···HCCH and I-···HCCH: results of coupled cluster calculations

Large-scale coupled cluster calculations at the CCSD(T) level of approximation have been carried out for the anionic complexes Br−···HCCH and I−···HCCH, both of which have a linear equilibrium structure. The equilibrium dissociation energies (De) are predicted to be 3126 and 2550 cm−1, respectively. Agreement with available experimental data, obtained through predissociation infrared spectroscopy, is very good. In addition, many predictions are made for spectroscopic properties of various isotopomers of the two species. Particular emphasis is given to the effects of vibrational anharmonicity, conveniently expressed by anharmonicity constants Xij and vibration–rotation coupling constants αr. Transition dipole moments were calculated for various stretching vibrational transitions.

The equilibrium structures of linear carbon clusters of type C 2 n +1 ( n = 1-4)

On the basis of large-scale coupled-cluster calculations including connected triple substitutions accurate equilibrium structures have been established for the linear carbon chain molecules with an odd number of carbon atoms up to C9. The individual equilibrium bond lengths are indicative of strong double bonds in all cases.

A theoretical investigation of the silicon-carbon chain molecule SiC8

Large-scale coupled cluster calculations have been carried out for linear SiC

The saddle point of the nucleophilic substitution reaction Cl − + CH 3 Cl: results of large-scale coupled cluster calculations

On the basis of large-scale coupled cluster calculations including connectedz triple substitutions in a perturbative way, the geometrical parameters of the D3h saddle point of the Walden inversion reaction Cl− + CH3Cl′→ ClCH3 + Cl′− are predicted to be Rs (C—Cl) = 2.301 A and rs (C—H) = 1.069 A. The barrier height with respect to the reactants is recommended to be 11.5 ± 1.0 kJ mol−1. Connected triple substitutions lower the barrier height by almost a factor of 2, but have very little influence on the geometric structure of the saddle point.

Coupled cluster calculations for HC7N, HC7NH+ and C7N, molecules of interest to astrochemistry

Large-scale coupled cluster calculations were carried out for linear HC7N, HC7NH+ and C7N (2Π and 2Σ states). Accurate equilibrium geometries (bond lengths accurate to better than 0·001 å) are established. The ground-state rotational constant of HC7 NH+ is predicted to be B 0= 553·8 ±0·5 MHz. Owing to its large equilibrium dipole moment of 6·35 D it may be a suitable candidate for forthcoming experimental investigation by microwave spectroscopy or radio astronomy. Various predictions are made for HC7N and HC7NH+ in order to facilitate their detection by means of infrared spectroscopy. Partially restricted open-shell coupled cluster calculations including connected triple substitutions yield the 2Π and 2Σ states of C7N to be very close in energy and substantial rovibronic interaction is expected.

Coupled cluster calculations for HC7N, HC7NH+ and C7N, molecules of interest to astrochemistry

Large-scale coupled cluster calculations were carried out for linear HC7N, HC7NH+ and C7N (2Π and 2Σ states). Accurate equilibrium geometries (bond lengths accurate to better than 0·001 å) are established. The ground-state rotational constant of HC7 NH+ is predicted to be B0= 553·8 ±0·5 MHz. Owing to its large equilibrium dipole moment of 6·35 D it may be a suitable candidate for forthcoming experimental investigation by microwave spectroscopy or radio astronomy. Various predictions are made for HC7N and HC7NH+ in order to facilitate their detection by means of infrared spectroscopy. Partially restricted open-shell coupled cluster calculations including connected triple substitutions yield the 2Π and 2Σ states of C7N to be very close in energy and substantial rovibronic interaction is expected.