Molecular structure is often considered as emerging from the decoherence effect of the environment. Electrons are part of the environment of the nuclei in a molecule. In this work, their contribution to the classical-like geometrical relationships often observed between nuclei in molecular systems is investigated. Reduced density matrix (RDM) elements are evaluated from electron-nucleus wave functions. The computational results show that the electrons play a role in the localization of the nuclei around specific geometries. Although the electronic environment alone cannot explain molecular symmetry-broken isomers, it can contribute to their dynamical stability by reducing off-diagonal RDM elements.
Many molecular "quantum" theories, like "quantum chemistry", conceal that they are actually quantum-classical approaches---they treat one set of molecular degrees of freedom classically while the remaining degrees of freedom follow the laws of quantum mechanics. We show that the prominent "frozen-nuclei approximation", which is often used in molecular control communities, is a further example for such theory reduction: It treats the nuclei of the molecule as classical particles. Here, we demonstrate that the ignorance about the quantum nature of nuclei has far-reaching consequences for the the…
For localized and oriented vibrationally excited molecules, the one-body probability density of the nuclei (one-nucleus density) is studied. Like the familiar and widely used one-electron density that represents the probability of finding an electron at a given location in space, the one-nucleus density represents the probability of finding a nucleus at a given position in space independent of the location of the other nuclei. In contrast to the full many-dimensional nuclear probability density, the one-nucleus density contains less information and may thus be better accessible by experiment, …
We have carried out a large scale computational investigation to assess the utility of common small-molecule force fields for computational screening of low energy conformers of typical organic molecules. Using statistical analyses on the energies and relative rankings of up to 250 diverse conformers of 700 different molecular structures, we find that energies from widely-used classical force fields (MMFF94, UFF, and GAFF) show unconditionally poor energy and rank correlation with semiempirical (PM7) and Kohn-Sham density functional theory (DFT) energies calculated at PM7 and DFT optimized geo…
The Two-Component Quantum Theory of Atoms in Molecules (TC-QTAIM): The unified theory of localization/delocalization of electrons, nuclei and exotic elementary particles
Recently a number of diatomic and polyatomics molecules has been identified as a prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows to decrease the kinetic energy of molecules down to microkelvin temperatures with high efficiency and then capture them to molecular traps, including magneto-optical trap. Trapped molecules can be used for creation of molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements and a multitude of other applications. Polyatomic molecules with heavy nuclei present considerable interest for th…
Two hybrid van der Waals density functionals (vdW-DFs) are constructed using 25%, Fock exchange with i) the consistent-exchange vdW-DF-cx functional and ii) with the vdW-DF2 functional. The ability to describe covalent and non-covalent binding properties of molecules are assessed. For properties related to covalent binding, atomization energies (G2-1 set), molecular reaction energies (G2RC set), as well as ionization energies (G21IP set) are benchmarked against experimental reference values. We find that hybrid-vdW-DF-cx yields results that are rather similar to those of the standard non-empir…
We have implemented and tested the method we have recently proposed [J. Phys. Chem. Lett. 10, 1537 (2019)] to treat dispersion interactions, which is derived from a supramolecular wavefunction constrained to leave the diagonal of the many-body density matrix of each monomer unchanged. The corresponding variational optimization leads to expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated monomers only, which provides a framework to build new approximations without the need for polarizabilities or virtual orbitals. The question we want to answe…
The accurate prediction of singlet and triplet excitation energies is of significant fundamental interest and is critical for many applications. An area of intense research, most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction…
The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e. those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM ana…
We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational ansatz for the correlated ground state of the fully interacting molecule/environment system. This wavefunction is optimized via variational Monte Carlo and the ground state energy is subsequently estimat…
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work …
Production and spectroscopy of cold radioactive molecules
California Institute of Technology（加州理工学院）；Yale University（耶鲁大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Massachusetts Institute of Technology（麻省理工学院）；Michigan State University（密歇根州立大学）
Dynamic nuclear polarization (DNP) is an NMR sensitivity enhancement technique that mediates polarization transfer from unpaired electrons to NMR-active nuclei. Despite its success in elucidating important structural information on biological and inorganic materials, the detailed polarization-transfer pathway-from the electrons to the nearby and then the bulk solvent nuclei, and finally to the molecules of interest-remains unclear. In particular, the nuclei in the paramagnetic polarizing agent play significant roles in relaying the enhanced NMR polarizations to more remote nuclei. Despite thei…
Interacting dipole ($p$) bosons along with scalar ($s$) bosons, based on the ideas drawn from the interacting boson model of atomic nuclei, led to the development of the vibron model based on $U(4)$ spectrum generating algebra for diatomic molecules. The $U(4) \supset SO(4) \supset SO(3)$ algebra generates rotation-vibration spectra. Extending this to two coupled $SO(4)$ algebras and three $SO(4)$ algebras describe triatomic and four-atomic molecules respectively. Similarly, appropriately coupled $U(2) \supset SO(2)$ algebras will describe the stretching vibrations, with proper point group sym…
We examine the performance of our recently developed LFAs-PBE exchange-correlation (XC) potential [C.-R. Pan, P.-T. Fang, and J.-D. Chai, Phys. Rev. A, 2013, 87, 052510] for the high-order harmonic generation (HHG) spectra and related properties of H2+ molecules aligned parallel and perpendicular to the polarization of an intense linearly polarized laser pulse, employing the real-time formulation of time-dependent density functional theory (RT-TDDFT). The results are compared with the exact solutions of the time-dependent Schrodinger equation as well as those obtained with other XC potentials …
We present benchmark integrated and differential cross-sections for electron collisions with H$_2$ using two different theoretical approaches, namely, the R-matrix and molecular convergent close-coupling (MCCC). This is similar to comparative studies conducted on electron-atom collisions for H, He and Mg. Electron impact excitation to the $b \ ^3Σ_u^+$, $a \ ^3Σ_g^+$, $B \ ^1Σ_u^+$, $c \ ^3Π_u$, $EF \ ^1Σ_g^+$, $C \ ^1Π_u$, $e \ ^3Σ_u^+$, $h \ ^3Σ_g^+$, $B' \ ^1Σ_u^+$ and $d \ ^3Π_u$ excited electronic states are considered. Calculations are presented in both the fixed nuclei and adiabatic nuc…
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the nuclei. For this picture, an elementary formalism of decoherence theory is developed and numerical results are presented for few-particle systems. The numerical examples suggest that the electron-nucleus Coulomb interaction is sufficient for inducing a blurred shape with strong quantum coherences in compounds of the lightest elements, H$_2$, D$_2$, T$_2$, and HeH…
Quantum Monte Carlo Calculations of Dihydrogen Binding Energetics on Ca Cations: an Assessment of Errors in Density Functionals for Weakly Bonded Systems
Assessment of density functional methods with correct asymptotic behavior
长程校正（LC）杂化泛函和渐近校正（AC）模型势是两种不同的具有正确渐近行为的密度泛函方法。已知它们对于对交换相关势的渐近线敏感的性质是准确的，例如分子的最高占据分子轨道能量和里德伯激发能。为了提供一个全面的比较，我们调查的性能，这两个计划和其他人在一个非常广泛的应用，包括渐近线问题，自相互作用误差问题，能隙问题，电荷转移问题，和许多其他。LC混合计划被证明是一贯优于AC模型潜在的计划。此外，为了与IP 131数据库中收集的分子一致[Y.- S. Lin，C.- W. Tsai，G.- D.李和J- D. Chai，J. Chem. Phys.，2012，136，154109]，我们扩展了EA 115和FG 115数据库，以分别包括另外16个分子的垂直电子亲合势和基本能隙，并开发了新的数据库AE 113（113原子化能量），其由IP 131中113个分子的原子化能量的精确参考值组成。这些数据库将有助于评估密度泛函方法的准确性。
We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order $1/c^0$, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.
Dipole moments are a simple, global measure of the accuracy of the electron density of a polar molecule. Dipole moments also affect the interactions of a molecule with other molecules as well as electric fields. To directly assess the accuracy of modern density functionals for calculating dipole moments, we have developed a database of 200 benchmark dipole moments, using coupled cluster theory through triple excitations, extrapolated to the complete basis set limit. This new database is used to assess the performance of 88 popular or recently developed density functionals. The results suggest …
Molecules containing superheavy atoms can be artificially created to serve as sensitive probes for study of symmetry-violating phenomena. Here, we provide a detailed theoretical study for diatomic molecules containing the superheavy lawrencium nuclei. The sensitivity to time-reversal violating properties was studied for different neutral and ionic molecules. The effective electric fields in these systems were found to be about 3-4 times larger than other known molecules on which electron electric dipole moment experiments are being performed. Similarly, these superheavy molecules exhibit an en…
In pre-Born-Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum chemistry treatment, which relies on the separation of the motion of the electrons and the atomic nuclei. A fully quantum mechanical treatment of molecules has a great promise for future developments and applications. Its most accurate versions may contribute to the definition of new schemes for metrology and testing fundamental physical theories; its approximate …
We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information of …
A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely quantum framework by defining a molecular orientation operator. Canonical rotational commutation relations are established explicitly. Moreover, physical constraints are imposed on the observables in order to define the state of a molecular system located in the neighborhood of the ground state defined by the equilibrium condition.
Molecules and atomic highly charged ions provide powerful low-energy probes of the fundamental laws of physics: Polar molecules possess internal fields suitable to enhance fundamental symmetry violation by several orders of magnitudes, whereas atoms in high charge states can feature large relativistic effects and compressed level structures, ideally posed for high sensitivity to variations of fundamental constants. Polar, highly charged molecules could benefit from both: large internal fields and large relativistic effects. However, a high charge dramatically weakens chemical bonding and drive…
Evaluation of potential energy of interaction between molecules using one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials
