Quantum chemistry simulation on quantum computers: theories and experiments

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.     

Quantum algorithm for alchemical optimization in material design

The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules obtainable from a set of atomic species grow exponentially with the size of the system, limiting the efficiency of classical sampling algorithms. On the other hand, quantum computers can provide an efficient solution to the sampling of the chemical compound space for the optimization of a given molecular property. In this work, we propose a quantum algorithm for addressing the material design problem with a favourable scaling. The core of this approach is the representation of the space of candidate structures as a linear superposition of all possible atomic compositions. The corresponding ‘alchemical’ Hamiltonian drives the optimization in both the atomic and electronic spaces leading to the selection of the best fitting molecule, which optimizes a given property of the system, e.g., the interaction with an external potential as in drug design. The quantum advantage resides in the efficient calculation of the electronic structure properties together with the sampling of the exponentially large chemical compound space. We demonstrate both in simulations and with IBM Quantum hardware the efficiency of our scheme and highlight the results in a few test cases. This preliminary study can serve as a basis for the development of further material design quantum algorithms for near-term quantum computers.

‘Alchemical’ quantum algorithm for the simultaneous optimisation of chemical composition and electronic structure for material design. By exploiting quantum mechanical principles this approach will boost drug discovery in the near future.     

He2@C60: Thoughts of the concept of a molecule and of the concept of a bond in quantum chemistry

We present a broad palette of discussions of the concepts of a molecule and a chemical bond that always lay down behind all computational modeling in quantum chemistry and of the endohedral fullerene He₂@C₆₀ in particular. For this purpose, we offer the definition of quantum chemistry as composed of three ingredients. Each of them is illustrated by its particular concept, either that of a molecule or a bond. The third, computational ingredient is tackled to resolve the bonding manifold of He₂@C₆₀ and to demonstrate that van‐der‐Waals binding of He? He is converted within He₂@C₆₀ into a stronger bond due to that C₆₀ acts as an electronic buffer and [He₂] moiety mimics a fractionally charged . Experimental fingerprints of He₂@C₆₀ are computed. © 2015 Wiley Periodicals, Inc.     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.     

Correct Modeling of Cisplatin: a Paradigmatic Case

Quantum chemistry is a useful tool in modern approaches to drug and material design, but only when the adopted model reflects a correct physical picture. Paradigmatic is the case of cis ‐diaminodichloroplatinum(II), cis ‐[Pt(NH₃)₂Cl₂], for which the correct simulation of the structural and vibrational properties measured experimentally still remains an open question. By using this molecule as a proof of concept, it is shown that state‐of‐the‐art quantum chemical calculations and a simple model, capturing the basic physical flavors, a cis ‐[Pt(NH₃)₂Cl₂] dimer, can provide the accuracy required for interpretative purposes. The present outcomes have fundamental implications for benchmark studies aiming at assessing the accuracy of a given computational protocol.     

Fullerene encapsulation with calix[5]arenes

This paper presents the synthesis of the fullerene hosts based on the calix[5]arenes and their binding properties. Calix[5]arenes 1a, 2, 3a bind C₆₀ or C₇₀ in organic solvents. The solvent effect of the fullerene complexation was clearly observed; the association constant decreases in a solvent with high solubility for C₆₀. Covalently linked double-calix[5]arenes 4-6 were also investigated on their binding properties for fullerenes in organic solvents. Their binding abilities for both C₆₀ and C₇₀ are extremely high in toluene solution. Higher binding selectivity toward C₇₀ is observed by all the double-calix[5]arenes. The selectivity of 5a toward C₇₀/C₆₀ is highest in toluene with a value of 10. The structures of the supramolecular complexes of the calix[5]arene hosts and C₆₀ or C₇₀ were investigated by using ¹H and ¹³C NMR studies. The molecular mechanics calculation and X-ray structure reveal that the interior of the calix[5]arene is complementary to the exterior of C₆₀ molecule. In contrast, the host-guest complexes of C₇₀ with the simple calix[5]arenes take many conformational options due to its less symmetric shape. The molecular mechanics calculation and our chemical shift simulation nicely worked to estimate the reliable structures; the calix[5]arene cavity takes up C₇₀ molecule, and the C₇₀ molecule tilts significantly from the C5 axis of the calix[5]arene. In the case of the host-guest complex of C₇₀ with the double-calix[5]arene, the molecular dynamics simulation of the host-guest complex represented the realistic movement of the bound C₇₀ inside the cavity. The combination of the molecular dynamics simulation and the chemical shift simulation of the host-guest complex suggested that the C₇₀ molecule rapidly moves inside the cavity.     

Electronic excitation in anionic polymerization of butadiene: Nonempirical calculations of reaction complexes

A new mechanism of anionic polymerization of butadiene is proposed. In the elementary chemical act, the “living” polymer–monomer complex is excited into the low‐lying triplet state. This state has the character of charge (electron) and cation (Li⁺ or Na⁺) transfer from the terminal unit of the active center to the monomer molecule. In the framework of this concept, the probability of chemical bond formation is determined by spin density on radical centers of reagent molecules. Semiempirical and ab initio 6‐31G** quantum‐chemical calculations showed stable interaction between components of the complex in the ground electronic state (9–11 kcal/mol) and low energy levels of triplet excited states (<14 kcal/mol). This new approach is shown to be useful in the analysis of polymerization kinetics and the microstructure of polybutadiene depending on the cation type and the ion pair state. The mechanism of cis‐trans isomerization in the terminal unit of the living polymer consists in concerted rotation about the C_β? C_γ bond and the migration of Li between C_α and C_γ atoms. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Longitudinal NLO properties of C2H2, HCCF,and C2F2: Electron correlation and vibration effects

Electron correlation and vibration effects on longitudinal nonlinear optical properties of acetylene (C₂H₂), fluoroacetylene (HCCF), and difluoroacetylene (C₂F₂) have been studied using various quantum chemistry methods, including the second‐order perturbation theory (MP2); coupled cluster approach with singles, doubles (CCSD), and noniterative triples (CCSD(T)); and density functional methods (B3LYP and B98). Evaluation of the static and dynamic vibration (nuclear relaxation) contributions was based on the finite field relaxation method. Particular attention has been devoted to the assessment of the electron correlation effects on the nuclear relaxation contributions to the molecular properties. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Calculation of the moscovium ground-state energy by quantum algorithms

We investigate the possibility to calculate the ground-state energy of the atomic systems on a quantum computer. For this purpose we evaluate the lowest binding energy of the moscovium atom with the use of the iterative phase estimation and variational quantum eigensolver (VQE). The calculations by the VQE are performed with a disentangled unitary coupled cluster ansatz and with various types of hardware-efficient ansatze. The optimization is performed with the use of the Adam and quantum natural gradients procedures. The scalability of the ansatze and optimizers is tested by increasing the size of the basis set and the number of active electrons. The number of gates required for the iterative phase estimation and VQE is also estimated.     

Quantum chemistry of ferroelectric solids: Electronic structures and peculiar behavior of zero‐dimensional K3H(SO4)2‐like materials

The main problems of quantum chemistry of H‐bonded ferroelectrics are treated using the zero‐dimensional K₃H(SO₄)₂‐like crystals as suitable examples. Various quantum chemical approaches and computational procedures are applied to evaluate the Ising model coupling parameters that determine different thermodynamic and dielectric properties of these materials. The calculated Ising parameters are employed to describe the peculiarities of ferroelectric behavior of the K₃H(SO₄)₂ family crystals in the framework of mean field approximation. The problems related to the H‐bond proton (deuteron) tunneling are also discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

An efficient synthesis of novel l-rhamnose based non-ionic surfactants under controlled microwave irradiation

The scope and limitations of microwave-assisted glycosylation for the preparation of various alkyl l-rhamnoside amphiphiles were investigated. Straightforward coupling of hydrophilic unprotected sugar and hydrophobic high molecular weight alcohols, in the presence of p-toluenesulfonic acid as a promoter, yielded structurally different compounds in very good yields (37–87%). A homologous series including 17 examples of alkyl α-l-rhamnoside amphiphiles varying in chain structure (C₄–C₂₀) is reported. The structures of the new derivatives were determined by NMR spectroscopy and quantum chemical calculations. Molecular geometry optimizations of different ring forms (¹C₄ and ⁴C₁) and anomeric configurations were carried out using DFT calculations. Herein we demonstrate the advantages of microwave irradiation for the preparation of a broad variety of linear and branched-chain alkyl α-l-rhamnosides. The application of this approach to the synthesis of new natural non-ionic surfactants makes this method attractive because of their potential use in biomedical and pharmaceutical chemistry.     

Role of quantum chemical calculations in molecular biophysics with a historical perspective

We discuss how the basic principles of quantum chemistry and quantum mechanics can be and have been applied to a variety of problems in molecular biophysics. First, the historical development of quantum concepts in biophysics is discussed. Next, we describe a series of interesting applications of quantum chemical methods for studying biologically active molecules, molecular structures, and some of the important processes which play a role in living organisms. We discuss the application of quantum chemistry to such processes as energy storage and transformation, and the transmission of genetic information. Quantum chemical approaches are essential to comprehend and understand the molecular nature of these processes. To conclude our work, we present a short discussion of the perspectives of quantum chemical methods in modern biophysics, the field of experimental and theoretical chiral vibrational and electronic spectroscopy.     

The Kernel energy method: Application to graphene and extended aromatics

The quantum chemistry of finite aperiodic graphene flakes is a matter of considerable interest because of the anticipated technological importance of such objects. Since real aperiodic graphene flakes will in general be composed of many thousands of carbon atoms, theoretical methods appropriate to such large molecules would need to be used for the ab initio quantum calculation of their properties. The Kernel energy method is discussed here, and it is shown to be accurately applicable to graphenes and analogous extended aromatic molecules. It is necessary to define the kernels of a graphene molecule in a new way because of the extensive aromaticity, which defines its electronic structure. The kernels used in the reconstruction of the full graphene sheet preserve the total number of π‐electrons, Clar sextets, and the approximate overall aromaticity. Sivaramakrishnan et al. [J Phys Chem A, 2005, 109, 1621] define similar “ring conserved isodesmic reactions (RCIR).” The principal innovation of this article is the suggestion that kernels may be mathematically extracted from an extended aromatic molecule such as graphene by a fissioning of aromatic bonds. Hartree Fock (HF) and Møller‐Plesset (MP2) chemical models using a Gaussian basis of 3‐21G orbitals are used to calculate the total energy of a graphene flake. This demonstration calculation is performed on a graphene flake in which dangling bonds are saturated with hydrogens (C₇₈H₂₆) composed of a total of 104 atoms arranged in 27 benzenoid rings. The KEM with both types of chemical model are shown to be accurate to nearly 1 kcal/mol, of a total energy, which is nearly 3000 atomic units, that is, with an absolute error within “chemical accuracy” and a relative error of the order of 5 × 10⁵% of the total energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A quantum chemical study of tricyclooctane and its congeners

A PBE0/6-311G(3d ₅ f ₇,p) quantum chemical method is used to determine the structural parameters of the molecules of sin- and anti-tricyclo[4.2.0.0^2.5]octane, [2.2.2]propellane, tricyclo[3.3.0.0^2.6]octane, prismanes (CH)_2n (n = 1–7), and dicubane C₁₂H₈. Bond lengths in anti-tricyclo[4.2.0.0^2.5]octane amount to 1.572 ?, The tetratomic ring in tricyclo[3.3.0.0^2.6]octane is a flattened tetrahedron with internuclear distances of 1.551? and 2.037 ?. The symmetry of C₈H₈ sin-tricyclo[4.2.0.0^2.5]octa-3,4,7,8-tetrayl moieties in prismanes and metal organic compounds (C₈H₈RhCl₂RhC₈H₈, C₈H₈RhCl₂RhC₇H₈, and C₈H₈PdCl₂) is higher than the symmetry of a free sin-tricyclo[4.2.0.0^2.5]octane molecule.