Coupled Cluster Singles Doubles Method Research Articles

Carbon Clusters: Thermochemistry and Electronic Structure at High Temperatures.

This paper studies the thermochemistry and electronic structure of small carbon clusters and hydrocarbons, which are major constituents of pyrolysis gases released into the boundary layer of ablating heat shields. Our focus lies on clusters of up to four carbon atoms. Among other molecules, thermochemistry data for molecules such as C3H and C4H have been determined using the Weizmann-1 (W1) method. These molecules have very limited thermochemistry data recorded in the literature, thereby necessitating new and accurate computations of required properties such as electronic energies of low-lying states, heats of formation, harmonic frequencies, and rotational constants. A study of electronically excited states of these molecules computed using the equations of motion coupled cluster singles doubles method revealed C4 and C4H to be potential sources of radiation absorption in the boundary layer. The excited electronic states of interest are studied further to obtain their optimum geometries, rotational constants, and vibrational frequencies. Moreover, we also study the effect of low-lying excited electronic states on the partition function to assess their effect on the thermodynamics of these pyrolysis gases in the high-temperature regime. Neglecting the excited electronic states records a maximum difference of 12% in the computed specific heat capacity values, Cp values. Finally, comparisons of the equilibrium mole fractions obtained using the thermodynamics computed in this paper with the existing state-of-the-art tables used for hypersonic applications (e.g., JANAF and Gurvich Tables) show an order of magnitude difference in the mixture compositions. It is shown that the rhombic isomer of C4 (1Ag), which is energetically close to the ground state (3Σg-) and usually neglected in composition calculations, contributes to a 28% increase in the equilibrium mole fraction of the C4 molecule.

Efficient self-consistent treatment of electron correlation within the random phase approximation

A self-consistent Kohn-Sham (KS) method is presented that treats correlation on the basis of the adiabatic-connection dissipation-fluctuation theorem employing the direct random phase approximation (dRPA), i.e., taking into account only the Coulomb kernel while neglecting the exchange-correlation kernel in the calculation of the Kohn-Sham correlation energy and potential. The method, denoted self-consistent dRPA method, furthermore treats exactly the exchange energy and the local multiplicative KS exchange potential. It uses Gaussian basis sets, is reasonably efficient, exhibiting a scaling of the computational effort with the forth power of the system size, and thus is generally applicable to molecules. The resulting dRPA correlation potentials in contrast to common approximate correlation potentials are in good agreement with exact reference potentials. The negatives of the eigenvalues of the highest occupied molecular orbitals are found to be in good agreement with experimental ionization potentials. Total energies from self-consistent dRPA calculations, as expected, are even poorer than non-self-consistent dRPA total energies and dRPA reaction and non-covalent binding energies do not significantly benefit from self-consistency. On the other hand, energies obtained with a recently introduced adiabatic-connection dissipation-fluctuation approach (EXXRPA+, exact-exchange random phase approximation) that takes into account, besides the Coulomb kernel, also the exact frequency-dependent exchange kernel are significantly improved if evaluated with orbitals obtained from a self-consistent dRPA calculation instead of an exact exchange-only calculation. Total energies, reaction energies, and noncovalent binding energies obtained in this way are of the same quality as those of high-level quantum chemistry methods, like the coupled cluster singles doubles method which is computationally more demanding.

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strength-dependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N(6) to N(5). Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Mo̸ller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.

Calculated Spectroscopy and Atmospheric Photodissociation of Phosphoric Acid

Detection of phosphine (PH(3)) gas in the upper troposphere suggests that the biogeochemical P cycle also includes an atmospheric component that consists of volatile phosphorus-containing molecules. A reasonable end product for the oxidation of PH(3) in the atmosphere is phosphoric acid (H(3)PO(4)). We propose that H(3)PO(4) may be photodissociated into HOPO(2) and H(2)O in the stratosphere, where H(3)PO(4) is likely to be present in gaseous form. We have calculated the energy barrier of this reaction and show that in addition to electronic transitions, OH-stretching overtone transitions can also provide the necessary energy. OH-stretching fundamental and overtone transitions were calculated with the use of an anharmonic oscillator local mode model. The probability of overtone induced photodissociation was estimated with molecular dynamical reaction coordinate simulations. Electronic transitions were calculated with the equation of motion coupled cluster singles doubles method. We have calculated the photodissociation rate constants for absorption of visible, UV, and Lyman-alpha radiation at altitudes from 20 to 100 km. We show that at altitudes between 30 and 70 km, the photodissociation of H(3)PO(4) is likely to proceed via absorption in the UV region by electronic transitions.

Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis

A production level implementation of the closed-shell local quadratic configuration interaction and coupled cluster methods with single and double excitations (QCISD and CCSD) based on the concept of pair natural orbitals [local pair natural orbital LPNO-QCISD and LPNO-CCSD) is reported, evaluated, and discussed. This work is an extension of the earlier developed LPNO coupled-electron pair approximation (LNPO-CEPA) method [F. Neese et al., Chem. Phys. 130, 114108 (2009)] and makes extended use of the resolution of the identity (RI) or density fitting (DF) approximation. Two variants of each method are compared. The less accurate approximations (LPNO2-QCISD/LPNO2-CCSD) still recover 98.7%-99.3% of the correlation energy in the given basis and have modest disk space requirements. The more accurate variants (LPNO1-QCISD/LPNO1-CCSD) typically recover 99.75%-99.95% of the correlation energy in the given basis but require the Coulomb and exchange operators with up to two-external indices to be stored on disk. Both variants have comparable computational efficiency. The convergence of the results with respect to the natural orbital truncation parameter (T(CutPNO)) has been studied. Extended numerical tests have been performed on absolute and relative correlation energies as function of basis set size and T(CutPNO) as well as on reaction energies, isomerization energies, and weak intermolecular interactions. The results indicate that the errors of the LPNO methods compared to the canonical QCISD and CCSD methods are below 1 kcal/mol with our default thresholds. Finally, some calculations on larger molecules are reported (ranging from 40-86 atoms) and it is shown that for medium sized molecules the total wall clock time required to complete the LPNO-CCSD calculations is only two to four times that of the preceding self-consistent field (SCF). Thus these methods are highly suitable for large-scale computational chemistry applications. Since there are only three thresholds involved that have been given conservative default values, the methods can be confidentially used in a "black-box" fashion in the same way as their canonical counterparts.

Förster Energy Transfer and Davydov Splittings in Time-Dependent Density Functional Theory: Lessons from 2-Pyridone Dimer.

The Davydov or exciton splitting of vertical excitation energies is commonly used to estimate the excitation energy transfer rate between chromophores. Here we investigate the S1-S2 Davydov splitting in 2-pyridone dimer as a function of the monomer separation, R. We assess the ability of various functionals to reproduce the Davydov splitting at finite R predicted by the approximate coupled cluster singles doubles method CC2. While semilocal functionals fail qualitatively because of spurious charge-transfer intruder states, global hybrids with a large fraction of exact exchange, such as BHandH-LYP, reproduce the CC2 splittings within few wavenumbers. We analyze our results by comparison to lowest-order intermolecular perturbation theory in the spirit of Förster and Dexter. At equilibrium hydrogen bond distance, the Förster-Dexter splittings are too small by up to a factor of 2.

Relativistic coupled-cluster single-double method applied to alkali-metal atoms

A relativistic version of the coupled-cluster single-double (CCSD) method is developed for atoms with a single valence electron. In earlier work, a linearized version of the CCSD method (with extensions to include a dominant class of triple excitations) led to accurate predictions for energies, transition amplitudes, hyperfine constants, and other properties of monovalent atoms. Further progress in high-precision atomic structure calculations for heavy atoms calls for improvement of the linearized coupled-cluster methodology. In the present work, equations for the single and double excitation coefficients of the Dirac-Fock wave function, including all nonlinear coupled-cluster terms that contribute at the single-double level, are worked out. Contributions of the nonlinear terms to energies, electric-dipole matrix elements, and hyperfine constants of low-lying states in alkali-metal atoms from Li to Cs are evaluated and the results are compared with other calculations and with precise experiments.