Electric, Magnetic, and Spectral Properties of H3+ Ground State Calculated from Single-Center Wavefunctions

Abstract

Single-center wavefunctions, employing up to 100 configuration-interaction terms, are used to compute electric, magnetic, and spectral properties of the A1′1 electronic ground state of equilateral triangular H3+. The best values for several computed properties are: electronic energy, E=−1.3405 hartree; equilibrium internuclear distance, R=1.65 bohr; electric quadrupole moment, Θzz= −1.2540 B; and Larmor contribution to the mean diamagnetic susceptibility, χ¯L=−3.2693×10−6 cgs·emu. Expectation values for the squared electronic coordinate operators 〈 x12〉, 〈 y12〉, 〈 z12〉, and 〈 r12〉 are also given. The derivative of the electric quadrupole moment with respect to symmetric motion of the nuclei was calculated to be ∂ Θzz/∂ R=−2.5531 B/Å, while the derivative of the electric dipole moment (center-of-mass origin) with respect to molecular bending was calculated to be ∂ μx/∂ φ=−0.0193 D/deg. These latter results permit prediction of the strengths of the quadrupole-allowed A1′ and dipole-allowed E′ vibrational fundamentals in the infrared spectrum. Finally, using excited-state wavefunctions and oscillator strengths reported previously, we have calculated the components of the electric dipole polarizability for the A1′1 state, αxx=αyy=0.4879 Å3, αzz=0.2567 Å3, α¯=0.4109 Å3.

Ground State of the H3+ Molecular Ion: Physics Behind

“…The major expectation values in Table IV , which holds for D 3h symmetric configurations, was first mentioned in [28]. Without doubt, the trial function (6) can be used to study the potential energy surface.…”

“…The trial function (16) is more accurate than all(!) traditional CI calculations which were performed before 1990 (see [26]) even including the one with the largest set of 100 configurations [27,28] 5 and as well as [32], however, being worse than the large GG calculation [34] 5 for a list of 42 calculations of the ground state energy of H + 3 in the period 1938-1992 see Ref. [26], for a list of selected ab-initio calculations till 1995, see [5] (700 configurations).…”

“…[27] CI-48; b CI wavefuncion (I) in Ref. [28]; c Correlated Gaussian (unrestricted) wavefunction with 15 terms in Ref. [24]; d CI wavefunction in Ref.…”

Precision mass ratio of He+3 to HD+

“…The corresponding statistical uncertainty for the average is in parentheses. The fifth column gives the correction due to imbalance in the cyclotron radii, with statistical uncertainty in this correction (see below), while the sixth column gives the correction [22] due to the large polarizability of HD + in its ro-vibrational ground state [23,24], and the small polarizability of H + 3 in its vibrational ground state [25,26], which contributes only 1 x 10 −12 to the CFR. TABLE I.…”

Rotational Energy as Mass in H3+ and Lower Limits on the Atomic Masses of D and He<

“…In the case of H + 3 (2), after measuring the CFR with respect to 3 He + , the 3 He + was removed and an HD + ion was then made within 0.2 mm of the axis of the trap, and so well inside the 2 mm radius cyclotron orbit of H + 3 (2). The sixth column gives the correction due to imbalance in the cyclotron radii (which results in different relativistic frequency shifts for the two ions), while the seventh gives the correction [5] due to the large polarizability of HD + in its ro-vibrational ground state [28,29], and the small polarizability of H + 3 in its vibrational ground state [30,31]. The last column gives the atomic mass differences between the ions, M[H + 3 ] − M[X + ], where X + = HD + or 3 He + , along with the statistical uncertainty, and systematic uncertainty, which we take to be 100% of the imbalance correction.…”