Implementation of Z-vector method in the relativistic coupled cluster framework to calculate first order energy derivatives: Application to SrF molecule
Sudip Sasmal, Himadri Pathak, Malaya K. Nayak, Nayana Vaval, Sourav Pal
The molecular dipole moment and magnetic hyperfine structure constant demand an accurate wavefunction far from the nucleus and in near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic coupled cluster theory to calculate the first order property of molecular systems in their open-shell ground state configuration. The implemented method is applied to calculate molecular dipole moment and parallel component of the magnetic hyperfine structure constant of SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of molecular dipole moment is in the accuracy of ~? 0.5 %, which is clearly an improvement over the previous calculation based on the expectation value method in the four component coupled cluster framework [V. S. Prasannaa et al, Phys. Rev. A 90, 052507 (2014)] and it is the best calculated value till date. Thus, it can be inferred that the Z vector method can provide an accurate wavefunction in both near and far nuclear region, which is evident from our calculated results.
We investigate the energetics of the atom exchange reaction in the SrF+alkali-metal atom and CaF+alkali-metal atom systems. Such reactions are possible only for collisions of SrF and CaF with the lithium atoms, while they are energetically forbidden for other alkali-metal atoms. Specifically, we focus on SrF interacting with Li, Rb, and Sr atoms and use ab initio methods to demonstrate that the SrF+Li and SrF+Sr reactions are barrierless. We present potential energy surfaces for the interaction of the SrF molecule with the Li, Rb, and Sr atoms in their energetically lowest-lying electronic spi…
We present a theoretical investigation of the chemical reaction SrF + SrF $\rightarrow$ products, focusing on reactions at ultralow temperatures. We find that bond swapping, SrF + SrF $\rightarrow$ Sr$_2$ + F$_2$, is energetically forbidden at these temperatures. Rather, the only energetically allowed reaction is SrF + SrF $\rightarrow$ SrF$_2$ + Sr, and even then only singlet states of the SrF$_2$ trimer can form. A calculation along a reduced reaction path demonstrates that this abstraction reaction is barrierless, and proceeds by one SrF molecule "handing off" a fluorine atom to the other m…
We report on the production, deceleration and detection of a SrF molecular beam. The molecules are captured from a supersonic expansion and are decelerated in the X$^2Σ^+ (v=0, N=1)$ state. We demonstrate the removal of up to 40% of the kinetic energy with a 2 meter long modular traveling-wave decelerator. Our results demonstrate a crucial step towards the preparation of ultracold gases of heavy diatomic molecules for precision spectroscopy.
We explore the suitability of ultracold collisions between spin-polarized SrF($^2Σ^+$) molecules and Rb($^2$S) atoms as elementary steps for the sympathetic cooling of SrF($^2Σ^+$) molecules in a magnetic trap. To this end, we carry out quantum mechanical scattering calculations on ultracold Rb+SrF collisions in a magnetic field based on an accurate potential energy surface for the triplet electronic state of Rb-SrF developed ab initio using a spin-restricted coupler cluster method with single, double and noniterative triple excitations [RCCSD(T)]. The Rb-SrF interaction has a global minimum w…
We demonstrate a scheme for optical cycling in the polar, diatomic molecule strontium monofluoride (SrF) using the $X ^2Σ^+\toA^2Π_{1/2}$ electronic transition. SrF's highly diagonal Franck-Condon factors suppress vibrational branching. We eliminate rotational branching by employing a quasi-cycling $N=1\to N^\prime=0$ type transition in conjunction with magnetic field remixing of dark Zeeman sublevels. We observe cycling fluorescence and deflection through radiative force of an SrF molecular beam using this scheme. With straightforward improvements our scheme promises to allow more than $10^5$…
We show that products of the isotopic substitution reactions in experimentally accessible molecules such as NaK, RbCs, and SrF are cold according to their translational energy below hundreds of mK. For these chemical reactions, molecular products may occupy only the lowest rotational states. We also discuss the possibility of controlling the chemical reactions by the electric field in ultracold mixtures of molecules and atoms with low kinetic energy release, where one of the constituent atoms of colliding molecule is replaced by its isotope. This letter opens new avenues in investigating the b…
It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields. Unfortunately laser cooling has not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for many applications. For example, heteronuclear molecules possess permanent electric dipole moments which lead to long-range, tunable, anisotropic dipole-dipole interactions. The combination of the dipole-dipole interaction and the precise control over molecular degrees of freedom …
Strong field ionization of benzene, fluorobenzene, benzonitrile and 1-chloro-2-fluorobenzene, is studied within the framework of real-space and real-time time-dependent density functional theory. Analysis of the ionization rates as function of the molecule orientation, reveal significant multielectron contribution from inner Kohn-Sham orbitals that depends on the electronic structure and on the orbital symmetries of the molecule, as well as on the polarization and intensity of the external laser field. Calculated photoelectron angular distributions at different molecule orientations and in res…
We report self-assembly and phase transition behavior of lower diamondoid molecules and their primary derivatives using molecular dynamic (MD) simulation and density functional theory (DFT) calculations. Two lower diamondoids (adamantane and diamantane), three adamantane derivatives (amantadine, memantine and rimantadine) and two artificial molecules (Adamantane+Na and Diamantane+Na) are studied separately in 125-molecule simulation systems. We performed DFT calculations to optimize their molecular geometries and obtain atomic electronic charges for the corresponding MD simulation, by which we…
The reliability of popular density functionals was studied for the description of torsional profiles of 36 molecules: glyoxal, oxalyl halides and their thiocarbonyl derivatives. HF and \textcolor{black}{eighteen} functionals of varying complexity, from local density to range-separated hybrid approximations and double-hybrid, have been considered and benchmarked against CCSD(T)-level rotational profiles. For molecules containing heavy halogens, all functionals except M05-2X and M06-2X fail to reproduce barrier heights accurately and a number of functionals introduce spurious minima. Dispersion …
Currently, quantum scattering calculations cannot be used for quantitative predictions of molecular scattering observables at ultralow temperatures. This is a result of two problems: the extreme sensitivity of the scattering observables to details of potential energy surfaces (PES) for interactions between the collision partners, and the exceedingly large size of molecular basis sets required for the numerically exact integration of the Schrödinger equation in the presence of external fields. Here, we suggest a new statistical approach to address both of the above problems. We show that ensemb…
There is substantial interest in producing samples of ultracold molecules for possible applications in quantum computation, quantum simulation of condensed matter systems, precision measurements, controlled chemistry, and high precision spectroscopy. A crucial step to obtaining large samples of ultracold, trapped molecules is developing a means to bridge the gap between typical molecular source velocities (~150-600 m/s) and velocities for which trap loading or confinement is possible (~5-20 m/s). Here we show deceleration of a beam of neutral strontium monofluoride (SrF) molecules using radiat…
The derivative discontinuity of the exchange-correlation functional of density-functional theory is cast as the difference of two types of electron affinities. We show that standard Kohn-Sham calculations can be used to calculate both affinities, and that their difference benefits from substantial and systematic error cancellations, permitting reliable estimates of the derivative discontinuity. Numerical calculations for atoms and molecules show that the discontinuity is quite large (typically several eV), and significantly and consistently improves the agreement of the calculated fundamental …
We present a theory for the temperature-dependent nuclear magnetic shielding tensor of molecules with arbitrary electronic structure. The theory is a generalization of Ramsey's theory for closed-shell molecules. The shielding tensor is defined as a second derivative of the Helmholtz free energy of the electron system in equilibrium with the applied magnetic field and the nuclear magnetic moments. This derivative is analytically evaluated and expressed as a sum over states formula. Special consideration is given to a system with an isolated degenerate ground state for which the size of the dege…
Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier $μ= \partial E/\partial N$ in the Euler-Lagrange variational equation for the ground state density as the chemical potential of the electrons. We first discuss why the Lagrange multiplier in this case is an arbitrary constant and therefore cannot be a physical characteristic of an atom or molecule. The switching of the energy derivative ("chemical potential") from $-I$ to $-A…
We present a data-driven approach for the prediction of the electric dipole moment of diatomic molecules, which is one of the most relevant molecular properties. In particular, we apply Gaussian process regression to a novel dataset to show that dipole moments of diatomic molecules can be learned, and hence predicted, with a relative error <5%. The dataset contains the dipole moment of 162 diatomic molecules, the most exhaustive and unbiased dataset of dipole moments up to date. Our findings show that the dipole moment of diatomic molecules depends on atomic properties of the constituents atom…
Density-Functional Theory (DFT) and Time-Dependent DFT Study of the Chemical and Physical Origins of Key Photoproperties of End-Group Derivatives of the Nonfullerene Bulk Heterojunction Organic Solar Cell Acceptor Molecule IDIC
Understanding electron transfer in organic molecules is of great interest in quantum materials for light harvesting, energy conversion, and integration of molecules into solar cells. This, however, poses the challenge of designing specific optimal molecular structure for which the processes of ultrafast quantum coherence and electron transport are not so well understood. In this work, we investigate subpicosecond time scale quantum dynamics and electron transfer in an efficient electron acceptor Rhodanine chromophoric complex. We consider an open quantum system approach to model the complex-so…
In this paper parent substances with molecules which can be divided into a skeleton and six univalent substituents, and that have the properties mentioned in the title, are considered. Two instances are the molecules of benzene and cyclopropane. The Lunn-Senior's symmetry groups of substitution isomerism of these compounds are described and upper bounds of the numbers of their di-substitution and tri-substitution homogeneous derivatives are found. Lists of the possible simple substitution reactions among di-substitution homogeneous derivatives, on one hand, and di-substitution heterogeneous, a…
Structures and minimum molecular electrostatic potential (MEP) distributions in anacardic acid and some of its derivatives have been studied by full geometry optimization at the M06-2X/6-31G(d,p), WB97XD/6-31G(d,p) and B3LYP/6-31G(d,p) levels of density functional theory (DFT) in gas phase as well as in DMSO and aqueous solutions. Solvent effect was treated employing the integral equation formalism of the polarizable continuum model. Effects of modifications of the C1-side chain on the minimum MEP values in various regions were studied. Minimum MEP values near the oxygen atoms of the C2-OH gro…
The probability of non-radiative transitions in photochemical dynamics is determined by the derivative couplings, the couplings between different electronic states through the nuclear degrees of freedom. Efficient and accurate evaluation of the derivative couplings is, therefore, of central importance to realize reliable computer simulations of photochemical reactions. In this work, the derivative couplings for multistate multireference second-order perturbation theory (MS-CASPT2) and its 'extended' variant (XMS-CASPT2) are studied, in which we present an algorithm for their analytical evaluat…
Diketopyrrolopyrroles are a popular class of electron-withdrawing unit in optoelectronic materials. When combined with electron donating side-chain functional groups such as thiophenes, they form a very broad class of donor-acceptor molecules: thiophene-diketopyrrolopyrroles (TDPPs). Despite their widescale use in biosensors and photovoltaic materials, studies have yet to establish the important link between the electronic structure of the specific TDPP and the critical optical properties. To bridge this gap, ultrafast transient absorption with 22 fs time resolution has been used to explore th…
In order to study electron-transfer mediated chemical processes on a metal surface, one requires not one but two potential energy surfaces (one ground state and one excited state) as in Marcus theory. In this letter, we report that a novel, dynamically-weighted, state-averaged constrained CASSCF(2,2) (DW-SA-cCASSCF(2,2)) can produce such surfaces for the Anderson Impurity model. Both ground and excited state potentials are smooth, they incorporate states with a charge transfer character, and the accuracy of the ground state surface can be verified for some model problems by renormalization gro…
We present quantum electron transport theory that incorporates dynamical effects of motion of atoms on electrode-molecule interfaces in the calculations of the electric current. The theory is based on non-equilibrium Green's functions. We separate time scales in the Green's functions on fast relative time and slow central time. The derivative with respect to the central time serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym equations for molecular Green's functions using Wigner representation and keep terms up to the second order with respect to the central time d…
Analytical Excited-State Gradients and Derivative Couplings in TDDFT with Minimal Auxiliary Basis Set Approximation and GPU Acceleration
ByteDance Seed（字节跳动种子）；New Cornerstone Science Laboratory, College of Chemistry and Molecular Engineering, Peking University（北京大学化学与分子工程学院新 Cornerstone 科学实验室）
We present a conspectus of recent joint spectroscopic and computational studies which provided novel insight into the photochemistry of hydrogen-bonded complexes of the heptazine (Hz) chromophore with hydroxylic substrate molecules (water and phenol). It was found that a functionalized derivative of Hz, tri-anisole-heptazine (TAHz), can photooxidize water and phenol in a homogeneous photochemical reaction. This allows the exploration of the basic mechanisms of the proton-coupled electron-transfer (PCET) process involved in the water photooxidation reaction in well-defined complexes of chemical…
This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree-Fock computations. A molecular-orbital-based (MOB) pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of molecular orbitals (MOs). The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant Gaussian pro…
Polycyclic aromatic compounds (PACs) constitute an important class of molecules found in various environments and are considered important pollutants of the Earth's atmosphere. In particular, functionalization of PACs modify the ring aromaticity, which greatly influences the chemical reactivity of these species. In this work we studied several oxygen-containing PACs, relevant to atmospheric chemistry. We investigated the conformational landscape of four naphthalene-derivative molecules -- namely ,1- and 2-hydroxynaphthalene and 1- and 2-naphthaldehyde -- by means of rotational and vibrational …
Aims. Due to the limitations of current computational technology, the fragmentation and isomerization products of vibrationally-excited polycyclic aromatic hydrocarbon (PAH) molecules and their derivatives are poorly studied. In this work, we investigate the intermediate products of PAHs and their derivatives as well as the gas-phase reactions relevant to the interstellar medium, with coronene as a case study. Methods. Based on the semi-empirical method of PM3 as implemented in the CP2K program, molecular dynamics simulations are performed to model the major processes (e.g., vibrations, fragme…
The derivative discontinuity is a key concept in electronic structure theory in general and density functional theory in particular. The electronic energy of a quantum system exhibits derivative discontinuities with respect to different degrees of freedom that are a consequence of the integer nature of electrons. The classical understanding refers to the derivative discontinuity of the total energy as a function of the total number of electrons ($N$), but it can also manifest at constant $N$. Examples are shown in models including several Hydrogen systems with varying numbers of electrons or n…
The relation between the derivative of the energy with respect to occupation number and the orbital energy, $\partial E/\partial n_i = ε_i$, was first introduced by Slater for approximate total energy expressions such as Hartree-Fock and exchange-only LDA, and his derivation holds for hybrid functionals as well. We argue that Janak's extension of this relation to (exact) Kohn-Sham density functional theory is not valid. The reason is the nonexistence of systems with noninteger electron number, and therefore of the derivative of the total energy with respect to electron number, $\partial E/\par…
We propose to evaluate the contribution of polycyclic aromatic hydrocarbon molecules that carry side groups to the mid-infrared emission spectra. Within this framework, the IR absorption spectra of 2- and 9-vinylanthracene were measured in Ar matrices at 12 K and in CsI and polyethylene pellets at room temperature. The laboratory spectra were analyzed with the support of simulations based on the density functional theory. For each PAH molecule, eight IR spectra were computed by combining the B3LYP functional with as many different basis sets, namely 4-31G, 4-31G(d), 6-31G, 6-311G, 6-31G(d), 6-…
We derive exact expressions for the forces and torques between biaxial molecules interacting via the RE-squared potential, a recent variant of the Gay-Berne potential. Moreover, efficient routines have been provided for rigid body MD simulations, resulting in 1.6 times speedup compared to the two-point finite difference approach. It has also been shown that the time cost of a MD simulation will be almost equal to a similar MC simulation, making use of the provided routines.
Quantum chemistry calculations such as the prediction of molecular properties and modeling of chemical reactions are a few of the critical areas where near-term quantum computers can showcase quantum advantage. We present a method to calculate energy derivatives for both ground state and excited state energies with respect to the parameters of a chemical system based on the framework of the variational quantum eigensolver (VQE). A low-depth implementation of quantum circuits within the hybrid variational paradigm is designed, and their computational costs are analyzed. We showcase the effectiv…
The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also…
The life cycle of the population of interstellar polycyclic aromatic hydrocarbon (PAH) molecules depends partly on the photostability of the individual species. We have studied the dissociative photoionization of two ethynyl-substituted PAH species, namely, 9-ethynylphenanthrene and 1-ethynylpyrene. Their adiabatic ionization energy and the appearance energy of fragment ions have been measured with the photoelectron photoion coincidence (PEPICO) spectroscopy technique. The adiabatic ionization energy has been found at 7.84 +/- 0.02 eV for 9-ethynylphenanthrene and at 7.41 +/- 0.02 eV for 1-eth…
We present a parametrization within a simplified LCAO model (a type of Hueckel model) for the description of $π$ molecular orbitals in organic molecules containing $π$-bonds between carbon, nitrogen, or oxygen atoms with $sp^2$ hybridization, which we show to be quite accurate in predicting the energy of the highest occupied $π$ orbital and the first $π$-$π*$ transition energy for a large set of organic compounds. We provide four empirical parameter values for the diagonal matrix elements of the LCAO description, corresponding to atoms of carbon, nitrogen with one $p_z$ electron, nitrogen with…
From the perspective of perturbation theory, we propose a systematic procedure for the evaluation of the derivative discontinuity (DD) of the exchange-correlation energy functional in Kohn-Sham density functional theory (KS-DFT), wherein the exact DD can in principle be obtained by summing up all the perturbation corrections to infinite order. Truncation of the perturbation series at low order yields an efficient scheme for obtaining the approximate DD. While the zeroth-order theory yields a vanishing DD, the first-order correction to the DD can be expressed as an explicit universal functional…
