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

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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).