Неэмпирический анализ изотопических сдвигов и резонансных эффектов в инфракрасном спектре высокого разрешения фреона-22 (CHF-=SUB=-2-=/SUB=-Cl), обогащенного -=SUP=-13-=/SUP=-C

The IR transmittance spectrum of an isotopic mixture of chlorodifluoromethane (CHF2Cl, Freon-22) with a 33% fraction of 13C and a natural ratio of chlorine isotopes was measured in the frequency range 1400-740 cm–1 with a resolution of 0.001 cm–1 at a temperature of 20C. An ab initio calculation of the structure and sextic potential energy surface and surfaces of the components of the dipole moment has been carried out by the the electronic quantum-mechanical method of Möller-Plesset, MP2/cc-pVTZ. Then the potential was optimized by replacing the harmonic frequencies with the frequencies calculated by the electronic method of coupled clusters, CCSD(T)/aug-cc-pVQZ. The fundamental and combination frequencies were calculated using the operator perturbation theory of Van Vleck (CVPTn) of the second and fourth order (n=2,4). Resonance effects were modeled using an additional variational calculation in the basis up to fourfold VCI excitation (4). The average prediction error for the fundamental frequencies of the 12C isotopologues was ~1.5 cm–1. The achieved accuracy made it possible to reliably predict the isotopic frequency shifts of the 13C isotopologues. It is shown that the strong Fermi resonance ν4/2ν6 dominates in the 12C isotopologues and is practically absent in 13C. The literature assumption [Spectrochim. Acta A, 44: 553] about the splitting of ν1 (CH) due to the resonance ν1/ν2+ν7+ν9 is confirmed. The coefficients of the polyadic quantum number are determined. The analysis made it possible to carry out a preliminary identification of the centers of the vibrational-rotational bands of isotopologues 13CHF235Cl и 13CHF237Cl in the spectrum of the mixture in preparation for individual analyzes of the vibrational-rotational structures of individual vibrational transitions.

Erratum: Why is the ground state electron configuration for Lithium 1s(2)2s ?

For the variational calculation involving the 1s22s state, we inadvertently filed energy contributions into the wrong categories, with the result that the Virial Theorem appeared to be violated. The overall calculation of the energy was done correctly, and appropriate assignment of the different energy contributions now confirms that the Virial Theorem is obeyed. Obviously, our conclusions are unchanged.

Variational Calculation of Lithium-Like Ions from B+2 to N+4 Using β-Type Roothaan–Hartree–Fock Wavefunction

Within the KaKB, KaLa, and KBLa shells in the position space, the properties of a series of three-electron systems, for instance, B+2, C+3, and N+4 ions, have been studied. This required the partitioning of the two-particle space-spin density and was explicit for the Hartree–Fock description which have been proposed by considering a basis set based on single-zeta B-type orbitals (BTOs). The one- and two-body radial electronic densities R(r1), R(r1, r2), moments ⟨rn1⟩, X-ray form factor F(s), nucleus density R(0), nuclear magnetic shielding constant qd, and the diamagnetic susceptibility бs in the position space are reported. Our results are realized via the Mathematica program and compared with previous theoretical values in the literature.

Quantum computed moments correction to variational estimates

The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor – Hamiltonian moments, ⟨Hn⟩. From these quantum computed moments, an estimate of the ground-state energy can be obtained using the ``infimum'' theorem from Lanczos cumulant expansions which manifestly corrects the associated variational calculation. With higher order effects in Hilbert space generated via the moments, the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5×5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infimum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.