arXiv subjects

Bogumił Jeziorski

Publications and source records attributed to Bogumił Jeziorski.

15 recordsLinked to original sources

arXiv2023

Relativistic treatment of diamagnetic susceptibility of helium

We report theoretical calculations of the diamagnetic susceptibility, $χ_0$, of helium atom. We determined the complete relativistic correction to $χ_0$ of the order of $α^4$, where $α$ is the fine structure constant, by including all $α^4$ terms originating from the Dirac and Breit equations for a helium atom in a static magnetic field. Finite nuclear mass corrections to $χ_0$ was also evaluated. To obtain very accurate results and reliable uncertainty estimates we used a sequence of explicitly correlated basis sets of fully optimized Slater geminals. We found that $χ_0=-2.119\,106(34)\cdot10^{-5}$ $a_0^3$ and $χ_0=-2.119\,400(34)\cdot10^{-5}$ $a_0^3$ for $^4$He and $^3$He isotopes, respectively, where $a_0$ is the Bohr radius and the uncertainties shown in the parentheses are due entirely to the very conservative estimate of the neglected QED corrections of the order of $α^5$. Our results are compared with the available experimental data and with previous, incomplete theoretical determinations of the $α^4$ contributions to the diamagnetic susceptibility of helium.

physics.atom-ph↗

arXiv2023

Diamagnetic susceptibility of neon and argon including leading relativistic effects

We report theoretical calculations of the static diamagnetic susceptibility, $χ_0$, of neon and argon atoms. The calculations were performed using a hierarchy coupled-cluster methods combined with application of both the Gaussian and Slater orbital basis sets. We included the complete relativistic correction of order of $α^4$, where $α$ is the fine structure constant, and obtained an estimate of the quantum electrodynamics (QED) contributions. The finite nuclear mass and size corrections were also considered but are found to be small. The final results are $χ_0=-8.4786(7)\cdot10^{-5}$ $a_0^3$ for the neon and $χ_0=-22.9545(32)\cdot10^{-5}$ $a_0^3$ for the argon atom, where $a_0$ is the Bohr radius. The uncertainties in the last digits, shown in the parentheses, are primarily due to the errors in the non-relativistic electronic wavefunction, as well as due to the neglected quantum electrodynamics corrections.

physics.atom-ph↗

arXiv2023

Ab initio Calculation of Fluid Properties for Precision Metrology

Recent advances regarding the interplay between ab initio calculations and metrology are reviewed, with particular emphasis on gas-based techniques used for temperature and pressure measurements. Since roughly 2010, several thermophysical quantities - in particular, virial and transport coefficients - can be computed from first principles without uncontrolled approximations and with rigorously propagated uncertainties. In the case of helium, computational results have accuracies that exceed the best experimental data by at least one order of magnitude and are suitable to be used in primary metrology. The availability of ab initio virial and transport coefficients contributed to the recent SI definition of temperature by facilitating measurements of the Boltzmann constant with unprecedented accuracy. Presently, they enable the development of primary standards of temperature in the range 2.5-552 K and pressure up to 7 MPa using acoustic gas thermometry, dielectric constant gas thermometry, and refractive index gas thermometry. These approaches will be reviewed, highlighting the effect of first-principles data on their accuracy. The recent advances in electronic structure calculations that enabled highly accurate solutions for the many-body interaction potentials and polarizabilities of atoms - particularly helium - will be described, together with the subsequent computational methods, most often based on quantum statistical mechanics and its path-integral formulation, that provide thermophysical properties and their uncertainties. Similar approaches for molecular systems, and their applications, are briefly discussed. Current limitations and expected future lines of research are assessed.

cond-mat.stat-mech↗

arXiv2023

First-principles calculation of the frequency-dependent dipole polarizability of argon

In this work we report state-of-the-art theoretical calculations of the dipole polarizability of the argon atom. Frequency dependence of the polarizability is taken into account by means of the dispersion coefficients (Cauchy coefficients) which is sufficient for experimentally relevant wavelengths below the first resonant frequency. In the proposed theoretical framework, all known physical effects including the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size corrections are accounted for. We obtained $α_0=11.0763(19)$ for the static polarizability and $α_2=27.976(15)$ and $α_4=95.02(11)$ for the second and fourth dispersion coefficients, respectively. The result obtained for the static polarizability agrees (within the estimated uncertainty) with the most recent experimental data [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)], but is less accurate. The dispersion coefficients determined in this work appear to be most accurate in the literature, improving by more than an order of magnitude upon previous estimates. By combining the experimentally determined value of the static polarizability with the dispersion coefficients from our calculations, the polarizability of argon can be calculated with accuracy of around $10\,$ppm for wavelengths above roughly $450\,$nm. This result is important from the point of view of quantum metrology, especially for a new pressure standard based on thermophysical properties of gaseous argon. Additionally, in this work we calculate the static magnetic susceptibility of argon which relates the refractive index of dilute argon gas with its pressure. While our results for this quantity are less accurate than in the case of the polarizability, they can provide, via Lorenz-Lorentz formula, the best available theoretical estimate of the refractive index of argon.

physics.chem-ph↗

arXiv2021

Path-integral calculation of the third dielectric virial coefficient of noble gases

We present the first framework for fully quantum calculation of the third dielectric virial coefficient $C_\varepsilon(T)$ of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework developed here will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

cond-mat.stat-mech↗

arXiv2021

Theoretical determination of polarizability and magnetic susceptibility of neon

We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value $α_0=2.66080(36)$ for the static polarizability, and $α_2=2.850(7)$ and $α_4=4.932(14)$ for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)], but our estimated uncertainty is significantly larger. For the dispersion coefficients, the results obtained in this work appear to be the most accurate to date overall compared to published theoretical and experimental data. We also calculated the static magnetic susceptibility of the neon atom, needed to obtain the refractive index of gaseous neon. Our result, $χ_0 = -8.484(19) \cdot 10^{-5}$ a.u., is about 9% larger in absolute value than the recommended experimental value [CRC Handbook of Chemistry and Physics, CRC Press, 2019, p. 4-145].

physics.atom-ph↗

arXiv2020

Second virial coefficients for helium-4 and helium-3 from accurate relativistic interaction potential

The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5 - 1000K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

physics.chem-ph↗

arXiv2019

Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function

In this communication we present a method of complete basis set (CBS) extrapolation of correlation energies obtained with a systematic sequence of one-electron basis sets. Instead of fitting the finite-basis results with a certain functional form, we perform analytic re-summation of the missing contributions coming from higher angular momenta, $l$. The assumption that they vanish asymptotically as an inverse power of $l$ leads to an expression for the CBS limit given in terms of the Riemann zeta function. This result is turned into an extrapolation method that is very easy to use and requires no "empirical" parameters to be optimized. The performance of the proposed method is assessed by comparing the results with accurate reference data obtained with explicitly correlated theories and with results obtained with standard extrapolation schemes. On average, the errors of the zeta-function extrapolation are several times smaller compared with the conventional schemes employing the same number of points. A recipe for estimation of the residual extrapolation error is also proposed.

physics.chem-ph↗

arXiv2019

Size consistency and counterpoise correction in explicitly correlated calculations of interaction energies and interaction-induced properties

Explicitly correlated calculations of interaction energies with wave functions that include all interparticle distances have suffered so far from the lack of size-consistency resulting from the difficulty to define monomer energies corresponding to the applied dimer basis. As a consequence it has not been possible to obtain interaction energies vanishing at infinite intermonomer distance $R$. This has dramatically reduced the accuracy of calculations at distances where the error in the dimer energy was comparable with the interaction energy itself. The same problem occurs in calculations of interaction-induced properties. In this communication we show how to circumvent this difficulty and obtain interaction energies or interaction-induced properties that vanish at large $R$. This is achieved by relaxing the Pauli principle in the diagonalization of the Hamiltonian of noninteracting monomers. The basis functions used for this diagonalization belong to the representation of the permutation group of the dimer induced by the product of representations appropriate for the monomer spin states. Nonlinear parameters of the basis set are optimized only for the dimer in the Pauli-allowed sector of the Hilbert space. In this way, one obtains $R$-dependent energy of noninteracting monomers and the corresponding interaction energy includes a counterpoise correction for the basis set superposition error. The efficiency of this procedure is demonstrated for the interaction of two hydrogen atoms where accurate reference data are known.

physics.chem-ph↗

arXiv2016

Determination of the exchange interaction energy from the polarization expansion of the wave function

The exchange contribution to the energy of the hydrogen atom interacting with a proton is calculated from the polarization expansion of the wave function using the conventional surface-integral formula and two formulas involving volume integrals: the formula of the symmetry-adapted perturbation theory (SAPT) and the variational formula recommended by us. At large internuclear distances $R$, all three formulas yield the correct expression $-(2/e)Re^{-R}$, but approximate it with very different convergence rates. In the case of the SAPT formula, the convergence is geometric with the error falling as $3^{-K}$, where $K$ is the order of the applied polarization expansion. The error of the surface-integral formula decreases exponentially as $a^K/(K+1)!$, where $a=\ln2 -\tfrac{1}{2}$. The variational formula performs best, its error decays as $K^{1/2} [a^{ K}/(K+1)!]^2$. These convergence rates are much faster than those resulting from approximating the wave function through the multipole expansion. This shows the efficiency of the partial resummation of the multipole series effected by the polarization expansion. Our results demonstrate also the benefits of incorporating the variational principle into the perturbation theory of molecular interactions.

quant-ph↗

arXiv2016

Convergence properties of the multipole expansion of the exchange contribution to the interaction energy

The conventional surface integral formula $J_{\rm surf}[Φ]$ and an alternative volume integral formula $J_{\rm var}[Φ]$ are used to compute the asymptotic exchange splitting of the interaction energy of the hydrogen atom and a proton employing the primitive function $Φ$ in the form of its truncated multipole expansion. Closed-form formulas are obtained for the asymptotics of $J_{\rm surf}[Φ_N]$ and $J_{\rm var}[Φ_N]$, where $Φ_N$ is the multipole expansion of $Φ$ truncated after the $1/R^N$ term, $R$ being the internuclear separation. It is shown that the obtained sequences of approximations converge to the exact results with the rate corresponding to the convergence radius equal to 2 and 4 when the surface and the volume integral formulas are used, respectively. When the multipole expansion of a truncated, $K$th order polarization function is used to approximate the primitive function the convergence radius becomes equal to unity in the case of $J_{\textrm{var}}[Φ]$. At low order the observed convergence of $J_{\rm var}[Φ_N]$ is, however, geometric and switches to harmonic only at certain value of $N=N_c$ dependent on $K$. An equation for $N_c$ is derived which very well reproduces the observed $K$-dependent convergence pattern. The results shed new light on the convergence properties of the conventional SAPT expansion used in applications to many-electron diatomics.

physics.chem-ph↗

arXiv2015

Exchange splitting of the interaction energy and the multipole expansion of the wave function

The exchange splitting $J$ of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula $J_{\textrm{surf}}[φ]$, the volume-integral formula of the symmetry-adapted perturbation theory $J_{\textrm{SAPT}}[φ]$, and a variational volume-integral formula $J_{\textrm{var}}[φ]$. The calculations are based on the multipole expansion of the wave function $φ$, which is divergent for any internuclear distance $R$. Nevertheless, the resulting approximations to the leading coefficient $j_0$ in the large-$R$ asymptotic series $J(R) = 2 e^{-R-1} R ( j_0 + j_1 R^{-1} + j_2 R^{-2} +\cdots ) $ converge, with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the $J_{\textrm{var}}[φ]$, $J_{\textrm{surf}}[φ]$, and $J_{\textrm{SAPT}}[φ]$ formulas are used, respectively. Additionally, we observe that also the higher $j_k$ coefficients are predicted correctly when the multipole expansion is used in the $J_{\textrm{var}}[φ]$ and $J_{\textrm{surf}}[φ]$ formulas. The SAPT formula $J_{\textrm{SAPT}}[φ]$ predicts correctly only the first two coefficients, $j_0$ and $j_1$, gives a wrong value of $j_2$, and diverges for higher $j_n$. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.

physics.chem-ph↗

arXiv2015

Asymptotics of the exchange splitting energy for a diatomic molecular ion from a volume integral formula of symmetry-adapted perturbation theory

The exchange splitting energy $J$ of the lowest \emph{gerade} and \emph{ungerade} states of the H$_2^+$ molecular ion was calculated using a volume integral expression of symmetry-adapted perturbation theory and standard basis set techniques of quantum chemistry. The performance of the proposed expression was compared to the well known surface integral formula. Both formulas involve the primitive function which we calculated employing either the Hirschfelder-Silbey perturbation theory or the conventional Rayleigh-Schrödinger perturbation theory (the polarization expansion). Our calculations show that very accurate values of $J$ can be obtained using the proposed volume integral formula. When the Hirschfelder-Silbey primitive function is used in both formulas the volume formula gives much more accurate results than the surface integral expression. We also show that using the volume integral formula with the primitive function approximated by Rayleigh-Schrödinger perturbation theory, one correctly obtains only the first four terms in the asymptotic expansion of the exchange splitting energy.

quant-ph↗

arXiv2015

Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer

In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order $α^2$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0$\,\pm\,$1.9 $cm^{-1}$, in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

physics.chem-ph↗

arXiv2013

On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions

In currently most popular explicitly correlated electronic structure theories the dependence of the wave function on the interelectronic distance rij is built via the correlation factor f(rij). While the short-distance behavior of this factor is well understood, little is known about the form of f(rij) at large rij. In this work we investigate the optimal form of f(r12) on the example of the helium atom and helium-like ions and several well-motivated models of the wave function. Using the Rayleigh-Ritz variational principle we derive a differential equation for f(r12) and solve it using numerical propagation or analytic asymptotic expansion techniques. We found that for every model under consideration, f(r12) behaves at large r12 as r12^ρ exp(B r12) and obtained simple analytic expressions for the system dependent values of ρ and B. For the ground state of the helium-like ions the value of B is positive, so that f(r12) diverges as r12 tends to infinity. The numerical propagation confirms this result. When the Hartree-Fock orbitals, multiplied by the correlation factor, are expanded in terms of Slater functions r^n exp(-βr), the numerical propagation reveals a minimum in f(r12) with depth increasing with N. For the lowest triplet state B is negative. Employing our analytical findings, we propose a new 'range-separated' form of the correlation factor with the short- and long-range r12 regimes approximated by appropriate asymptotic formulas connected by a switching function. Exemplary calculations show that this new form of f(r12) performs somewhat better than the correlation factors used thus far in the standard R12 or F12 theories.

quant-ph↗