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As quantum hardware continues to improve, more and more application scientists have entered the field of quantum computing. However, even with the rapid improvements in the last few years, quantum devices, especially for quantum chemistry applications, still struggle to perform calculations that classical computers could not calculate. In lieu of being able to perform specific calculations, it is important have a systematic way of estimating the resources necessary to tackle specific problems. Standard arguments about computational complexity provide hope that quantum computers will be useful for problems in quantum chemistry but obscure the true impact of many algorithmic overheads. These overheads will ultimately determine the precise point when quantum computers will perform better than classical computers. We have developed QREChem to provide logical resource estimates for ground state energy estimation in quantum chemistry through a Trotter-based quantum phase estimation approach. QREChem provides resource estimates which include the specific overheads inherent to problems in quantum chemistry by including heuristic estimates of the number of Trotter steps and number of necessary ancilla, allowing for more accurate estimates of the total number of gates. We utilize QREChem to provide logical resource estimates for a variety of small molecules in various basis sets, obtaining estimates in the range of $10^7-10^{15}$ for total number of T gates. We also determine estimates for the FeMoco molecule and compare all estimates to other resource estimation tools.

Repulsive short-range and attractive long-range van der Waals (vdW) forces have an appreciable role in the behavior of extended molecular systems. When using empirical force fields - the most popular computational methods applied to such systems - vdW forces are typically described by Lennard-Jones-like potentials, which unfortunately have a limited predictive power. Here, we present a universal parameterization of a quantum-mechanical vdW potential, which requires only two free-atom properties - the static dipole polarizability $\alpha_1$ and the dipole-dipole $C_6$ dispersion coefficient. This is achieved by deriving the functional form of the potential from the quantum Drude oscillator (QDO) model, employing scaling laws for the equilibrium distance and the binding energy as well as applying the microscopic law of corresponding states. The vdW-QDO potential is shown to be accurate for vdW binding energy curves, as demonstrated by comparing to ab initio binding curves of 21 noble-gas dimers. The functional form of the vdW-QDO potential has the correct asymptotic behavior both at zero and infinite distances. In addition, it is shown that the damped vdW-QDO potential can accurately describe vdW interactions in dimers consisting of group II elements. Finally, we demonstrate the applicability of the atom-in-molecule vdW-QDO model for predicting accurate dispersion energies for molecular systems. The present work makes an important step towards constructing universal vdW potentials, which could benefit (bio)molecular computational studies.

Quantum electrodynamic fields possess fluctuations corresponding to transient particle/antiparticle dipoles, which can be characterized by a non-vanishing polarizability density. Here, we extend a recently proposed quantum scaling law to describe the volumetric and radial polarizability density of a quantum field corresponding to electrons and positrons and derive the Casimir self-interaction energy (SIE) density of the field, $\bar{E}_{\rm{SIE}}$, in terms of the fine-structure constant. The proposed model obeys the cosmological equation of state $w=-1$ and the magnitude of the calculated $\bar{E}_{\rm{SIE}}$ lies in between the two recent measurements of the cosmological constant $\Lambda$ obtained by the Planck Mission and the Hubble Space Telescope., Comment: 6 pages

The quantum Drude oscillator (QDO) is an efficient yet accurate coarse-grained approach that has been widely used to model electronic and optical response properties of atoms and molecules, as well as polarization and dispersion interactions between them. Three effective parameters (frequency, mass, charge) fully characterize the QDO Hamiltonian and are adjusted to reproduce response properties. However, the soaring success of coupled QDOs for many-atom systems remains fundamentally unexplained and the optimal mapping between atoms/molecules and oscillators has not been established. Here, we present an optimized parametrization (OQDO) where the parameters are fixed by using only dipolar properties. For the periodic table of elements as well as small molecules, our OQDO model accurately reproduces atomic (spatial) polarization potentials and multipolar dispersion coefficients, elucidating the high promise of the presented model in the development of next-generation quantum-mechanical force fields for (bio)molecular simulations., Comment: 6 pages, 3 figures

Simulating molecules using the Variational Quantum Eigensolver method is one of the promising applications for NISQ-era quantum computers. Designing an efficient ansatz to represent the electronic wave function is crucial in such simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD) ansatz tends to have a large number of insignificant terms that do not lower the energy of the system. In this work, we present a unitary selective coupled-cluster method, a way to construct a unitary coupled-cluster ansatz iteratively using a selection procedure with excitations up to fourth order. This approach uses the electronic Hamiltonian matrix elements and the amplitudes for excitations already present in the ansatz to find the important excitations of higher order and to add them to the ansatz. The important feature of the method is that it systematically reduces the energy error with increasing ansatz size for a set of test molecules. The main advantage of the proposed method is that the effort to increase the ansatz does not require any additional measurements on a quantum computer.

By means of quantum mechanics and quantum electrodynamics applied to coupled harmonic Drude oscillators, we study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions, as considered within the employed Drude model for both non-retarded and retarded regimes. For the first case, we present an exact solution for two coupled oscillators obtained by diagonalizing the corresponding quantum-mechanical Hamiltonian and demonstrate that the external field can control the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by quantum electrodynamics, our analysis shows that field-induced electrostatic and polarization energies remain unchanged (in isotropic and homogeneous vacuum) compared to the nonretarded case. For interacting species modeled by quantum Drude oscillators, the developed framework based on quantum mechanics and quantum electrodynamics yields the leading contributions to molecular interactions under the combined action of external and vacuum fields., Comment: 23 pages, 3 figures

We employ various quantum-mechanical approaches for studying the impact of electric fields on both nonretarded and retarded noncovalent interactions between atoms or molecules. To this end, we apply perturbative and non-perturbative methods within the frameworks of quantum mechanics (QM) as well as quantum electrodynamics (QED). In addition, to provide a transparent physical picture of the different types of resulting interactions, we employ a stochastic electrodynamic approach based on the zero-point fluctuating field. Atomic response properties are described via harmonic Drude oscillators - an efficient model system that permits an analytical solution and has been convincingly shown to yield accurate results when modeling non-retarded intermolecular interactions. The obtained intermolecular energy contributions are classified as field-induced (FI) electrostatics, FI polarization, and dispersion interactions. The interplay between these three types of interactions enables the manipulation of molecular dimer conformations by applying transversal or longitudinal electric fields along the intermolecular axis. Our framework combining four complementary theoretical approaches paves the way toward a systematic description and improved understanding of molecular interactions when molecules are subject to both external and vacuum fields., Comment: 23 pages, 10 figures; some slight improvement in comparison to the preceding version

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schr\"{o}dinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by choice of the variational ansatz used to represent the trial wave function. Hence, the construction of efficacious ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing effective ansatzes that fall into two categories -- chemistry inspired and hardware efficient -- that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

The structure and stability of atomic and molecular systems with van der Waals (vdW) bonding are often determined by the interplay between attractive dispersion interactions and repulsive interactions caused by electron confinement. Arising due to different mechanisms -- electron correlation for dispersion and the Pauli exclusion principle for exchange-repulsion -- these interactions do not appear to have a straightforward connection. In this paper, we use a coarse-grained approach for evaluating the exchange energy for two coupled quantum Drude oscillators and investigate the mutual compensation of the attractive and repulsive forces at the equilibrium distance within the multipole expansion of the Coulomb potential. This compensation yields a compact formula relating the vdW radius of an atom to its multipole polarizabilities, $R_{\rm vdW} = A_l^{\,}\, \alpha_l^{{2}/{7(l+1)}}$, where $l$ is the multipole rank and $A_l$ is a conversion factor. Such a relation is compelling because it connects an electronic property of an isolated atom (atomic polarizability) with an equilibrium distance in a dimer composed of two closed-shell atoms. We assess the accuracy of the revealed formula for noble-gas, alkaline-earth, and alkali atoms and show that the $A_l$ can be assumed to be universal constants. Besides a seamless definition of vdW radii, the proposed relation can also be used for the efficient determination of atomic multipole polarizabilities solely based on the corresponding dipole polarizability and the vdW radius. Finally, our work provides a basis for the construction of efficient and minimally-empirical interatomic potentials by combining multipolar interatomic exchange and dispersion forces on an equal footing., Comment: 15 pages, 4 figures

Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, $\alpha$, rely on different scaling laws $\alpha \propto$ $R^3$, $R^4$, or $R^7$, for various definitions of the system radius $R$. Here, we consider a range of single-particle quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law $\alpha = C (4 \mu q^2/\hbar^2)L^4$, where $\mu$ and $q$ are the (effective) particle mass and charge, $C$ is a dimensionless excitation-energy ratio, and the characteristic length $L$ is defined via the $\mathcal{L}^2$-norm of the position operator. %The applicability of this unified formula is demonstrated by accurately predicting the dipole polarizability of 36 atoms and 1641 small organic~molecules. This unified formula is also applicable to many-particle systems, as shown by} accurately predicting the dipole polarizability of 36 atoms, 1641 small organic \rrr{molecules, and Bloch electrons in periodic systems., Comment: 3 figures are included

Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, a quantum computer-based AIMD method is presented. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. We compute the energy gradients numerically using the Hellmann-Feynman theorem, finite differences, and a correlated sampling technique. Our method only requires additional classical calculations of electron integrals for each degree of freedom, without any additional computations on a quantum computer beyond the initial VQE run. To achieve comparable accuracy, our gradient calculation method requires three to five orders of magnitude fewer measurements than other brute force methods without correlated sampling. As a proof of concept, AIMD dynamics simulations are demonstrated for the H2 molecule on IBM quantum devices. To the best of our knowledge, it is the first successful attempt to run AIMD on quantum devices for a chemical system. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction (FCI) wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular and material systems.

We examine the recently derived quantum-mechanical relation between atomic polarizabilities and equilibrium internuclear distances in van der Waals (vdW) bonded diatomic systems [Phys. Rev. Lett. {\bf 121}, 183401 (2018)]. For homonuclear dimers, this relation is described by the compact formula $\alpha_{\rm m}^{\rm q} = \Phi R_{\rm vdW}^7$, where the constant factor in front of the vdW radius was determined empirically. Here, we derive $\Phi = (4\pi\epsilon_0/a_0^4) \times \alpha^{4/3}$ expressed in terms of the vacuum electric permittivity $\epsilon_0$, the Bohr radius $a_0$, and the fine-structure constant $\alpha$. The validity of the obtained formula is confirmed by estimating the value of the fine-structure constant from non-relativistic quantum-mechanical calculations of atomic polarizabilities and equilibrium internuclear vdW distances. The presented derivation allows to interpret the fine-structure constant as the ratio between the polarizability densities of vacuum and matter, whereas the vdW radius becomes a geometrical length scale of atoms endowed by the vacuum field., Comment: 5 pages

One of the most important properties influencing the chemical behavior of an element is the energy released with the addition of an extra electron to the neutral atom, referred to as the electron affinity (EA). Among the remaining elements with unknown EA is astatine, the purely radioactive element 85. Astatine is the heaviest naturally occurring halogen and its isotope $^{211}$At is remarkably well suited for targeted radionuclide therapy of cancer. With the At$^-$ anion being involved in many aspects of current astatine labelling protocols, the knowledge of the electron affinity of this element is of prime importance. In addition, the EA can be used to deduce other concepts such as the electronegativity, thereby further improving the understanding of astatine's chemistry. Here, we report the first measurement of the EA for astatine to be 2.41578(7)eV. This result is compared to state-of-the-art relativistic quantum mechanical calculations, which require incorporation of the electron-electron correlation effects on the highest possible level. The developed technique of laser-photodetachment spectroscopy of radioisotopes opens the path for future EA measurements of other radioelements such as polonium, and eventually super-heavy elements, which are produced at a one-atom-at-a-time rate.

We start closing a gap in the comparison of experimental and theoretical data associated with the spin Hall effect. Based on a first-principles characterization of electronic structure and a semiclassical description of electron transport, we compute the skew-scattering contribution to the transverse spin and charge currents generated by spin and anomalous Hall effect in a Co/Cu multilayer system doped with Bi impurities. The fact that the created currents cross the interface between the two materials strongly influences the efficiency of charge to spin current conversion, as demonstrated by our results.

We consider an extrinsic contribution to the anomalous and spin Hall effect in dilute alloys based on Fe, Co, Ni, and Pt hosts with different substitutional impurities. It is shown that a strong skew-scattering mechanism is absent in such crystals with multi-sheeted Fermi surfaces. Based on this finding, we conclude on the mutual exclusion of strong intrinsic and skew-scattering contributions to the considered transport phenomena. It also allows us to draw general conditions for materials where the anomalous Hall effect caused by the skew scattering can be achieved giant.

The atomic dipole polarizability, $\alpha$, and the van der Waals (vdW) radius, $R_{\rm vdW}$, are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently and separately from each other. Here, we derive the quantum-mechanical relation $R_{\rm vdW} = const. \times\alpha^{1/7}$ which is markedly different from the common assumption $R_{\rm vdW} \propto \alpha^{1/3}$ based on a classical picture of hard-sphere atoms. As shown for 72 chemical elements between hydrogen and uranium, the obtained formula can be used as a unified definition of the vdW radius solely in terms of the atomic polarizability. For vdW-bonded heteronuclear dimers consisting of atoms $A$ and $B$, the combination rule $\alpha = (\alpha_A + \alpha_B)/2$ provides a remarkably accurate way to calculate their equilibrium interatomic distance. The revealed scaling law allows to reduce the empiricism and improve the accuracy of interatomic vdW potentials, at the same time suggesting the existence of a non-trivial relation between length and volume in quantum systems., Comment: Main manuscript (6 pages, 1 table , 3 figures) + Supplemental material (11 pages, 4 tables, 2 figures)

We present a theory of the Seebeck effect in nanomagnets with dimensions smaller than the spin diffusion length, showing that the spin accumulation generated by a temperature gradient strongly affects the thermopower. We also identify a correction arising from the transverse temperature gradient induced by the anomalous Ettingshausen effect and an induced spin-heat accumulation gradient. The relevance of these effects for nanoscale magnets is illustrated by ab initio calculations on dilute magnetic alloys., Comment: 5 pages, 2 figures

The challenging problem of skew scattering for Hall effects in dilute ferromagnetic alloys, with intertwined effects of spin-orbit coupling, magnetism and impurity scattering, is studied here from first principles. Our main aim is to identify chemical trends and work out simple rules for large skew scattering in terms of the impurity and host states at the Fermi surface, with particular emphasis on the interplay of the spin and anomalous Hall effects in one and the same system. The predicted trends are benchmarked by referring to three different \emph{ab initio} methods based on different approximations with respect to the electronic structure and transport properties., Comment: 5 pages, 4 figures

We calculate the potential energy curves, the permanent dipole moment curves, and the lifetimes of the ground and excited vibrational states of the heteronuclear alkali dimers XY (X, Y = Li, Na, K, Rb, Cs) in the X1{\Sigma}+ electronic state using the coupled cluster with singles doubles and triples (CCSDT) method. All-electron quadruple-{\zeta} basis sets with additional core functions are used for Li and Na, and small-core relativistic effective core potentials with quadruple-{\zeta} quality basis sets are used for K, Rb and Cs. The inclusion of the coupled cluster non-perturbative triple excitations is shown to be crucial for obtaining the accurate potential energy curves. Large one-electron basis set with additional core functions is needed for the accurate prediction of permanent dipole moments. The dissociation energies are overestimated by only 14 cm-1 for LiNa and by no more than 114 cm-1 for the other molecules. The discrepancies between the experimental and calculated harmonic vibrational frequencies are less than 1.7 cm-1, and the discrepancies for the anharmonic correction are less than 0.1 cm-1. We show that correlation between atomic electronegativity differences and permanent dipole moment of heteronuclear alkali dimers is not perfect. To obtain the vibrational energies and wave functions the vibrational Schr\"odinger equation is solved with the B-spline basis set method. The transition dipole moments between all vibrational states, the Einstein coefficients and the lifetimes of the vibrational states are calculated. We analyze the decay rates of the vibrational states in terms of spontaneous emission, and stimulated emission and absorption induced by black body radiation. In all studied heteronuclear alkali dimers the ground vibrational states have much longer lifetimes than any excited states.

We predict spin Hall angles up to 80% for ultrathin noble metal films with substitutional Bi impurities. The colossal spin Hall effect is caused by enhancement of the spin Hall conductivity in reduced sample dimension and a strong reduction of the charge conductivity by resonant impurity scattering. These findings can be exploited to create materials with high efficiency of charge to spin current conversion by strain engineering., Comment: 4 pages, 5 figures

We present a detailed analysis of the skew-scattering contribution to the spin Hall conductivity using an extended version of the resonant scattering model of Fert and Levy [Phys. Rev. Lett. {\bf 106}, 157208 (2011)]. For $5d$ impurities in a Cu host, the proposed phase shift model reproduces the corresponding first-principles calculations. Crucial for that agreement is the consideration of two scattering channels related to $p$ and $d$ impurity states, since the discussed mechanism is governed by a subtle interplay between the spin-orbit and potential scattering in both angular-momentum channels. It is shown that the potential scattering strength plays a decisive role for the magnitude of the spin Hall conductivity.

Two years after the prediction of a giant spin Hall effect for the dilute Cu(Bi) alloy [Gradhand et al., Phys. Rev. B 81, 245109 (2010)], a comparably strong effect was measured in thin films of Cu(Bi) alloys by Niimi et al. [Phys. Rev. Lett. 109, 156602 (2012)]. Both theory and experiment consider the skew-scattering mechanism to be responsible, however they obtain opposite sign for the spin Hall angle. Based on a detailed analysis of existing theoretical results, we explore differences between theory and experiment., Comment: 11 pages, 2 figures

Ballistic conductance through a single atom adsorbed on a metallic surface and probed by a scanning tunneling microscope (STM) tip can be decomposed into eigenchannel contributions, which can be potentially obtained from shot noise measurements. Our density functional theory calculations provide evidence that transmission probabilities of these eigenchannels encode information on the modifications of the adatom's local density of states caused by its interaction with the STM tip. In the case of open shell atoms, this can be revealed in nonmonotonic behavior of the eigenchannel's transmissions as a function of the tip-adatom separation., Comment: 4.5 pages, 5 figures, REVTeX

A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin current density a Kubo-St\v{r}eda-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker (KKR) band structure method in combination with the Coherent Potential Approximation (CPA) allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-scattering contribution of the SHC using the Boltzmann equation demonstrate the equivalence to the Kubo formalism in the dilute alloy regime and support the suggested decomposition scheme.