Fourth-order Many-body Perturbation Theory Research Articles

Multicomponent MP4 and the inclusion of triple excitations in multicomponent many-body methods.

This study implements the full multicomponent third-order (MP3) and fourth-order (MP4) many-body perturbation theory methods for the first time. Previous multicomponent studies have only implemented a subset of the full contributions, and the present implementation is the first multicomponent many-body method to include any connected triples contribution to the electron-proton correlation energy. The multicomponent MP3 method is shown to be comparable in accuracy to the multicomponent coupled-cluster doubles method for the calculation of proton affinities, while the multicomponent MP4 method is of similar accuracy as the multicomponent coupled-cluster singles and doubles method. From the results in this study, it is hypothesized that the relative accuracy of multicomponent methods is more similar to their single-component counterparts than previously assumed. It is demonstrated that for multicomponent MP4, the fourth-order triple-excitation contributions can be split into electron-electron and electron-proton contributions and the electron-electron contributions ignored with very little loss of accuracy of protonic properties.

Intermolecular interaction energies from fourth order many-body perturbation theory. Impact of individual electron correlation contributions.

The performance of Møller-Plesset perturbation theory methods for describing intermolecular interaction energies has been investigated with the focus on illuminating the impact of individual electron correlation energy contributions in fourth order. It is shown that a physically meaningful decomposition of the fourth order correlation energy can be obtained by grouping individual correlation energy terms that share the same diagrammatic loop structure. This decomposition of the fourth order singles (S), doubles (D), triples (T), and quadruples (Q) terms revealed that individual terms from each excitation class can have a huge impact on the energy that is much larger than the total fourth order correlation contribution. A partial summation of S, D, and Q terms has been derived that can reproduce the full fourth order interaction energies with a good accuracy and which does not include the computationally expensive triples energy term.

Padé-resummed fourth-order many-body perturbation theory: Applications to the description of Au–Au, Au–Hg, and Hg–Hg bonds

Pilot applications of Padé-resummed fourth-order many-body perturbation theory to the description of chemical bonds with strong contributions from the interactions of filled d-shells (Au–Au, Au–Hg, and Hg–Hg) are reported. The employed Padé approximants, especially the constrained [0/1,1] quadratic one, ensure radical improvements of accuracy with respect to the partial summation. The non-separability problem is discussed and bypassed through the direct resummation of perturbative expansions for differential correlation energies.

Electron correlation and properties of many-electron systems

Different computational methods of quantum chemistry, which are currently employed in accurate calculations of atomic and molecular properties, are discussed and their advantages and disadvantages are investigated in calculations of electric properties of Be, FH, and H2O. A complete fourth-order many-body perturbation theory (MBPT) approach based on the coupled Hartree–Fock (CHF) solution for the perturbed problem reveals that in several cases the fourth-order correlation correction to the CHF result is dominated by those terms which involve triply substituted intermediate states. Moreover, in some cases a complete fourth-order MBPT result appears to be inferior to those obtained in approximate MBPT treatments which involve only certain classes of intermediate states. Hence, a complete fourth-order MBPT approach may not be sufficient for accurate predictions of atomic and molecular properties. The applicability of the complete active space (CAS) SCF method is studied in calculations of electric properties of FH. Although this method offers some advantages over the MBPT approach, its usefulness may be limited by the requirement of rather large active orbital spaces which have to be used in order to achieve sufficiently high accuracy. The CAS SCF results can be improved by using multireference CI methods with reference functions built of the CAS SCF natural orbitals. A good performance of the MBPT method limited to singly and doubly substituted intermediate states suggests that reasonable results can also be obtained in similar configuration interaction (CI) calculations, provided the latter are corrected for the erratic treatment of unlinked clusters. It is shown that the unlinked cluster corrections due to Davidson and Siegbahn result in reasonable estimates of the total correlation contribution to different properties. Because of its fairly routine character the CI method limited to single and double substitutions may in this way provide useful data with relatively small computational effort.

MBPT and DFT Study of Hydrogen Cyanide Borane(1) Oligomers and Dehydrogenated Analogues

Geometry optimizations and fragmentation energies of the series of hydrogen cyanide borane(1) oligomers (up to hexamers) and their dehydrogenated analogues are presented. Structural parameters are examined at different computational levels: MBPT(2) (second-order many-body perturbation theory), SDQ-MBPT(4) (fourth-order many-body perturbation theory limited to singly-, doubly-, and quadruply excited configurations), and DFT-B3LYP (density functional theory with Becke's three-parameter hybrid functional using the Lee−Yang−Parr correlation functional). These oligomers seem to be suitable input for the models of the polymer chain because of their periodic structure emerging from successive HCNBH or HCNB addition. The stability of the oligomers in terms of initial “cracking” of the weakest bond is fairly high, ranging from 97 to 443 kJ/mol for the HCNBH series and from 329 to 589 kJ/mol for the HCNB series.

A systematic study of basis set, electron correlation, and geometry effects on the electric multipole moments, polarizability, and hyperpolarizability of HCl

The electric multipole moments, dipole and quadrupole polarizability and hyperpolarizability of hydrogen chloride have been determined from an extensive and systematic study based on finite-field fourth-order many-body perturbation theory and coupled-cluster calculations. Our best values for the dipole, quadrupole, octopole and hexadecapole moment at the experimental internuclear separation of Re=2.408 645a0 are μ=0.4238ea0, Θ=2.67ea02, Ω=3.94ea03, and Φ=13.37ea04, respectively. For the mean and the anisotropy of the dipole polarizability ααβ we recommend ᾱ=17.41±0.02 and Δα=1.60±0.03e2a02Eh−1. For the mean value of the first dipole hyperpolarizability βαβγ we advance β̄=−6.8±0.3e3a03Eh−2. Extensive calculations with a [8s6p6d3f/5s4p2d1f] basis set at the CCSD(T) level of theory yield the R-dependence of the Cartesian components and the mean of the second dipole hyperpolarizability γαβγδ(R)/e4a04Eh−3 around Re as γzzzz(R)=1907+1326(R−Re)+570(R−Re)2+10(R−Re)3−40(R−Re)4, γxxxx(R)=3900+747(R−Re)−65(R−Re)2−38(R−Re)3−7(R−Re)4, γxxzz(R)=962+222(R−Re)+88(R−Re)2+49(R−Re)3+5(R−Re)4, γ̄(R)=3230+841(R−Re)+151(R−Re)2+21(R−Re)3−9(R−Re)4, with z as the molecular axis. The present investigation suggests an estimate of (26.7±0.3)×102e4a04Eh−3 for the Hartree–Fock limit of the mean value γ̄ at Re. CCSD(T) calculations with basis sets of [8s6p6d3f/5s4p2d1f] and [9s7p5d4f/6s5p4d1f] size and MP4 calculations with the even larger [15s12p7d3f/12s7p2d1f] give (7.0±0.3)×102e4a04Eh−3 for the electron correlation effects for this property, thus leading to a recommended value of γ̄=(33.7±0.6)×102e4a04Eh−3. For the quadrupole polarizability Cαβ,γδ/e2a04Eh−1 at Re our best values are Czz,zz=41.68, Cxz,xz=26.11, and Cxx,xx=35.38, calculated with the [9s7p5d4f/6s5p4d1f] basis set at the CCSD(T) level of theory. The following CCSD(T) values were obtained with [8s6p6d3f/5s4p2d1f] at Re: dipole-quadrupole polarizability Aα,βγ/e2a03Eh−1, Az,zz=14.0, and Ax,zx=3.75, dipole-octopole polarizability Eα,βγδ/e2a04Eh−1, Ez,zzz=20.0, and Ex,xxx=3.0, and dipole-dipole-quadrupole hyperpolarizability Bαβ,γδ/e3a04Eh−2, Bzz,zz=−277, Bxz,xz=−261, Bxx,zz=246, and Bxx,xx=−416. A comparison of the mean polarizability and hyperpolarizability of some 18-electron systems shows that ᾱ(H2S)>ᾱ(HCl)>ᾱ(HOOH)>ᾱ(HOF)>ᾱ(Ar)>ᾱ(F2), and γ̄(H2S)>γ̄(HCl)>γ̄(HOOH)>γ̄(HOF)≈γ̄(Ar)>γ̄(F2).

Geometries and energies of small aluminium clusters in fcc symmetry

Small aluminium clusters as fragments of fcc lattice have been studied from an ab initio point of view. Complete geometry optimizations have been carried out at the fourth-order many-body perturbation theory level. Resulting geometric and electronic structure data have been compared with other results available in the literature. Possible clusters have been identified for future studies of chemisorption of different molecules on the aluminium surface. For the (100) surface is a `good' cluster, while for the (110) surface (5, 0) appears to be a `good' cluster. For the (111) surface, (3, 3, 2) appears to be an ideal cluster for future studies of chemisorption.

A cluster study of Rb atom chemisorption on a GaAs(110) surface

Different possible adsorption sites of rubidium atoms on a GaAs(110) surface have been investigated using ab-initio self-consistent Hartree - Fock energy cluster calculations followed by detailed correlation investigations at the level of fourth-order many-body perturbation theory. The Hay - Wadt effective core potentials have been used to represent the cores of the rubidium, gallium and arsenic atoms. We find that the Rb atom adsorption at a site modelled with a cluster is most favoured energetically followed by Rb adsorption at a site modelled with a cluster. Significant charge transfer from the Rb atom to the GaAs surface is also found to occur, with Ga atoms losing charge and As atoms gaining charge. Finally, comparisons are made among different alkali atom adsorptions on the GaAs(110) surface.

Coupled-cluster calculations of nuclear magnetic resonance chemical shifts

Theory and implementation of the gauge-including atomic orbital (GIAO) ansatz for the gauge-invariant calculation of nuclear magnetic resonance chemical shifts are described for the coupled-cluster singles and doubles (CCSD) approach. Results for the shielding constants of the hydrides HF, H2O, NH3, and CH4 as well as for a few multiply bonded systems such as CO, N2, and HCN demonstrate the importance of higher-order correlation corrections, as good agreement with experiment is only obtained at the CCSD level and to some extent at partial fourth-order many-body perturbation theory [SDQ-MBPT(4)] with the latter slightly overestimating correlation effects due to single and double excitations. For relative chemical shifts, GIAO-CCSD calculations provide in difficult cases (e.g., CO and CF4) more accurate results than previous GIAO-MBPT(2) calculations. But, it seems that it is often more important to include rovibrational effects (as well as possible molecule–solvent interactions) than higher-order correlation corrections. Despite that, GIAO-CCSD proves to be a powerful tool for the accurate calculation of NMR chemical shifts. Its capabilities as well as its limitations are demonstrated in shielding calculations for formaldehyde, diazomethane, and ozone. At least for the latter, the description provided by the CCSD ansatz is not sufficient and even higher excitations need to be considered.

Structural and electronic properties of trans-polysilene (SiH)x: Many-body perturbation theory versus density-functional methods.

The possibility of a Peierls-type lattice dimerization was investigated in trans-polysilene (SiH${)}_{\mathit{x}}$ by ab initio quantum-mechanical methods that provided results for polyacetylene previously in complete agreement with experiments. Electron correlation was treated in the fourth order of many-body perturbation theory (MBPT) as well as, for the purpose of comparison, by using different versions of density-functional theory (DFT). The classical electrostatic interaction in itself produced a dimerized ground state for (SiH${)}_{\mathit{x}}$ in the Hartree approximation. The bond alternation was somewhat increased by exchange at the Hartree-Fock (HF) level (\ensuremath{\Delta}${\mathit{r}}_{\mathrm{HF}}$=0.1392 \AA{}) and substantially reduced by electron correlation (\ensuremath{\Delta}${\mathit{r}}_{\mathrm{MP}4}$=0.0805 \AA{}). The HF dimerization energy of -40 meV per SiH unit was also diminished to -17 meV at the MP4 level. Gradient-corrected DFT potentials provided results for both the structural and energetic parameters in excellent agreement with those of the fourth-order MBPT. Though the HF value of the forbidden energy gap (4.04 eV) was reduced to 1.32 eV for correlated quasiparticles, (SiH${)}_{\mathit{x}}$ still remained an intrinsic semiconductor at all theoretical levels.

Electron correlation in extended systems: Fourth-order many-body perturbation theory and density-functional methods applied to an infinite chain of hydrogen atoms.

Linear equidistant and bond-alternating infinite chains of hydrogen atoms have been investigated by the ab initio crystal-orbital method at the Hartree-Fock (HF) level, by including electron correlation up to the complete fourth order of the Mo/ller-Plesset perturbation theory (MP4-PT), and by using different versions of density-functional theory (DFT). The Bloch functions have been expanded in all cases in a series of high-quality atomic-orbital basis sets and complemented by extended sets of polarization functions up to 6s3p2d1f per H atom. In order to compare the performance of the PT and DFT methods, several physical properties have been computed at all theoretical levels including lattice geometry, cohesive energy, mechanisms of bond alternation (Peierls instability), and energetic features of nonequilibrium configurations (dissociation). For these latter quantities, both spin-restricted (RHF) and unrestricted (UHF) wave functions have been employed in all orders of PT. The methods described have been used parallel to infinite chains and to the ${\mathit{H}}_{2}$ molecule, to be able to check their accuracy on experiments. In the case of the DFT, six different functionals (combining Slater and Becke exchange with local and gradient-corrected correlation potentials) have been utilized to test their accuracy in comparison with the MP4 results.

GIAO-MBPT(3) and GIAO-SDQ-MBPT(4) calculations of nuclear magnetic shielding constants

The gauge-including atomic orbital approach for the calculation of NMR chemical shifts has been implemented at third- and fourth-order many-body perturbation theory with the latter restricted to single, double, and quadruple excitations. Results obtained for HF, H 2O, NH 3, CH 4, CO, N 2, HCN, and F 2 suggest that higher-order effects in the perturbative treatment of electron correlation are important for the accurate theoretical prediction of nuclear magnetic shielding constants.

Electric dipole hyperpolarizability and quadrupole polarizability of methane from finite-field coupled cluster and fourth-order many-body perturbation theory calculations

We rely on a finite-field approach to calculate the static dipole (α) and quadrupole ( C) polarizability and the first (β) and second (γ) dipole hyperpolarizability of methane. Our best, CCSD(T) values for a α, β and the mean value of γ and C, obtained at R e =2.052 a o with a (11s7p4d2f/6s2p1d)[6s4p4d2f/4s2p1d] basis set, are α=16.39 e 2 a o 2 E h −1, β=−8.31 e 3 a o 3 E h −2, γ =2312 e 4 a o −3 and C =60.45 e 2 a o 4 E h −1. The derivatives of α, β and γ (symmetric stretch) and R e were calculated at the SDQ-MP4 level of theory with a (11s7p4d1f/6s2p1d) [6s4p4d1f/4s2p1d] basis set: (dα/d R) e=15.7 e 2 a o E h −1, (dβ/d R) e=−25.3 e 3 a o 2 E h −2 and (d γ/d R) e=37.4×10 2 e 4 a o 4 E h −3.

On the electronic structures of GaAs clusters

Ab initio molecular orbital theory is used to investigate the electronic and geometric structures of GaxAsy (x=y, 1<or=x<or=4) clusters. Correlation calculations are performed at the fourth-order many-body perturbation theory level. The ground state structure of Ga2As2 is found to be a rhombus, of Ga3As3, a Ga-capped trigonal bipyramid and, of Ga4As4, a rhombic prism. Electronic states, binding energies, ionization potentials and electron affinities of the clusters are presented and, wherever possible, compared with other published data in the literature. Mulliken population analysis indicates that the bonding in GaAs clusters is of a mixed type.

The interaction of a sodium atom with the silicon(111) surface

The interaction of a sodium atom with the silicon(111) surface is studied from the point of view of molecular orbital theory. The Si surface is modelled by finite clusters and the interaction of the alkali atom is investigated from different approach positions. Electron correlation is incorporated by invoking the concepts of fourth-order many-body perturbation theory. The results are compared with available data in the literature.

Double and quadruple zeta contracted Gaussian basis sets for hydrogen through neon

Koga and Thakkar's reoptimized (9s5p) and (12s7p) Gaussian basis sets for the atoms Li to Ne are contracted to [4s2p] and [7s4p], respectively, and their (4s) and (6s) sets for H and He are contracted to [2s] and [4s], respectively. The basis sets are tested by performing self-cosistent-field (SCF) geometry optimizations on LiH, BeH2, B2H6, CH4, NH3, H2O, and HF. The equilibrium geometries of hydrogen peroxide and hydrazine are determined at both the SCF and fourth-order many-body perturbation theory level. © 1993 John Wiley & Sons, Inc.

Electric multipole moments of ethene

The author reports finite-field self-consistent field (SCF) and fourth-order many-body perturbation theory (MP4) calculations of the electric quadrupole and hexadecapole moments of ethane (H2C2CH2). The best values (with C2C on the z axis and the molecule on the xz plane) are Theta xx1.197, Theta yy=-2.434 and Theta zz=1.237 ea02. Phi xxxx=-14.91, Phi yyyy=16.89 and Phi zzzz=-14.05 ea04.

Accurate dipole polarizability for Cl2(X1Σ+g)

Finite-field self-consistent field and fourth-order many-body perturbation theory with single, double and quadruple substitutions from the reference wavefunction calculations are reported for the static dipole polarizability (ααβ) of chlorine CL2(X1Σ+ g). The R/a0 dependence of the mean dipole polarizability (α) and the anisotropy (Δα) around the experimental equilibrium bond length of R e = 3.756776a0 is very well approximated by , . The present estimates of αzz, αxx, α and Δα at the ground vibrational state are 42·29, 25·32, 30·98 and 16·97e2a2 0E-1 h, respectively and should be the most accurate theoretical values currently available.

Stabilities of adsorption sites and charge transfers at the K/Si(001) surface.

Various adsorption models of a K atom on the Si(001) surface including the top-site model, and the charge transfer between K and Si have been exhaustively investigated using accurate ab initio self-consistent unrestricted Hartree-Fock total-energy calculations with the Hay-Wadt effective core potentials. Several cluster models of bare and hydrogen-bonded silicon atoms used to simulate the different possible adsorption sites on the Si(001) surface have been examined. The structural relaxation of the substrate on adsorption of K atoms has been accounted for by optimizing all the atomic positions of the adsorbed and substrate atoms. Also, the effects of electron correlation have been included by invoking the concepts of fourth-order many-body perturbation theory and these are found to be crucial in determining the preferred adsorption sites. Population analyses up to the many-body perturbation theory at the second level of all the models studied consistently show that the charge transferred from the K atom to Si lies between 0.12e and 0.40e. This charge transfer combined with the values of the K-Si bond lengths obtained in our calculations tend to suggest a polarized covalent bonding for the K/Si(001) system.

Quadrupole polarizability and hyperpolarizability of carbon monoxide

We report a study of the electric dipole-quadrupole (A α,β,γ), quadrupole-quadrupole (C α,β,γδ), dipole-octopole (E α,βγδ) polarizability and the dipole-dipole-quadrupole (B α,β,γδ) hyperpolarizability of carbon monoxide. All values are obtained from finite-field self-consistent field (SCF) and fourth-order manybody perturbation theory (MP4) calculations. Our best values for the dipole-octopole polarizability areE z,zzz=60.19 andE x,xxx=−38.06e 2 a 0 4 E h −1 . For the dipole-dipole-quadrupole hyperpolarizability we reportB zz,zz=−296,B xz,xz=−170,B xx,zz=88 andB xx,xx=−178e 3 a 0 4 E h −2 .