Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers

Quantum computing has recently exhibited great potential in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from the limitations of the size and the fidelity of near-term quantum hardware, the accurate simulation of large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method—the density matrix embedding theory, which respectively reduces the circuit depth and the problem size, we present a means to circumvent the limitations and demonstrate the potential of near-term quantum computers toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C₆H₈ and the equilibrium geometry of the C₁₈ molecule, using basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C₁₈ molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices.

Quantum embedding simulation greatly enhanced the capability of near-term quantum computers on realistic chemical systems and reach accuracy comparable to advanced quantum chemistry methods.     

An innovative computational comparison of exact and centrifugal sudden quantum properties of the N + N2 reaction

The development of an innovative computational strategy suited to provide an accurate quantum evaluation of the detailed properties of the N + N(2) exchange reaction has been undertaken by carrying out an extended theoretical study of such reaction. To this end exact and approximate quantum calculations (based on both time-independent and time-dependent techniques) of state-specific and state-to-state probabilities of the title reaction have been performed by considering values of the total angular momentum quantum number up to 20, values of total energy up to 2.3 eV and by making a combined use of both high throughput and high performance computing platforms. The comparison of the results obtained from calculations performed by taking into account the full Coriolis coupling of the allowed helicity states with those obtained when neglecting the Coriolis coupling or even a model energy shift treatment has allowed us to find out when a workflow managing the distribution of the jobs can replace exact treatments with approximate ones and for what type of properties this is possible.     

An automated approach for the parameterization of accurate intermolecular force‐fields: Pyridine as a case study

An automated protocol is proposed and validated, which integrates accurate quantum mechanical calculations with classical numerical simulations. Intermolecular force fields, (FF) suitable for molecular dynamics (MD) and Monte Carlo simulations, are parameterized through a novel iterative approach, fully based on quantum mechanical data, which has been automated and coded into the PICKY software, here presented. The whole procedure is tested and validated for pyridine, whose bulk phase, described through MD simulations performed with the specifically parameterized FF, is characterized by computing several of its thermodynamic, structural, and transport properties, comparing them with their experimental counterparts. © 2011 Wiley Periodicals, Inc.     

Application of semiempirical quantum chemical methods as a scoring function in docking

A crucial point in docking simulations is the scoring function used for estimation of the target-ligand interaction energy. The usual practice is to employ fast but simplified empirical scoring functions. Rigorous quantum chemical methods are too slow to screen virtual combinatorial libraries consisting of thousands of molecules, but they can be used in the final step of the simulations for assessing the results obtained. At this stage quantum chemical calculations can be performed only for the 10–100 top binders predicted by simplified scoring functions, and only using linear-scaling semiempirical quantum chemical methods such as MOZYME. The possibilities and potentialities of the quantum chemical methods for estimation of the binding affinities in docking simulations are a largely unexplored area, so the main goal of this study is a detailed evaluation of the potential and limitations of the MOZYME methodology for estimation of the target-ligand binding energies and its comparison with available experimental data.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Density-Functional Theory of Vibrations in Ni<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>V<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Clusters

We have performed the calculation of the vibrational frequencies, Fermi energy and binding energy for several clusters of Ni and vanadium atoms by using the first principles. The calculations are performed by using the density-functional theory in the local-density approximation with spin polarized orbitals. The calculation of vibrational frequencies shows that some of the clusters have positive vibrational frequencies which describe the oscillations of the stable clusters. The negative vibrational frequencies indicate that these clusters are instable with respect to these vibrations when no energy of this frequency is supplied. We find that for vanadium concentration less than 11.1% the clusters of Ni and V atoms are not stable. Hence ferromagnetism in Ni is predicted below 11.1% vanadium. We find the vibrational frequencies of several clusters for which the vanadium concentration is more than 11.1%. We are able to find a phase transition by use of quantum mechanics alone without the use of classical mechanical variables or thermodynamic variables such as temperature.     

Density functional theory treatment of electron correlation in the nuclear-electronic orbital approach

This paper presents the nuclear-electronic orbital density functional theory [NEO-DFT(ee)] method for including electron-electron correlation and nuclear quantum effects self-consistently in quantum chemical calculations. The NEO approach is designed to treat a relatively small number of nuclei quantum mechanically, while the remaining nuclei are treated classically. In the NEO-DFT(ee) approach, the correlated electron density is used to obtain the nuclear molecular orbitals, and the resulting nuclear density is used to obtain the correlated electron density during an iterative procedure that continues until convergence of both the nuclear and electronic densities. This approach includes feedback between the correlated electron density and the nuclear wavefunction. The application of this approach to bihalides and acetylene indicates that the nuclear quantum effects do not significantly impact the electron correlation energy, but the quantum nuclear energy is enhanced in the NEO-DFT(ee) B3LYP method. The excellent agreement of the NEO-DFT(ee)-optimized bihalide structures with the vibrationally averaged geometries from grid-based quantum dynamical methods provides validation for the NEO-DFT(ee) approach. Electron-proton correlation could be included by the development of an electron-nucleus correlation functional. Alternatively, explicit electron-proton correlation could be included directly into the NEO self-consistent-field framework with Gaussian-type geminal functions.     

Self‐consistent field for fragmented quantum mechanical model of large molecular systems

Fragment‐based linear scaling quantum chemistry methods are a promising tool for the accurate simulation of chemical and biomolecular systems. Because of the coupled inter‐fragment electrostatic interactions, a dual‐layer iterative scheme is often employed to compute the fragment electronic structure and the total energy. In the dual‐layer scheme, the self‐consistent field (SCF) of the electronic structure of a fragment must be solved first, then followed by the updating of the inter‐fragment electrostatic interactions. The two steps are sequentially carried out and repeated; as such a significant total number of fragment SCF iterations is required to converge the total energy and becomes the computational bottleneck in many fragment quantum chemistry methods. To reduce the number of fragment SCF iterations and speed up the convergence of the total energy, we develop here a new SCF scheme in which the inter‐fragment interactions can be updated concurrently without converging the fragment electronic structure. By constructing the global, block‐wise Fock matrix and density matrix, we prove that the commutation between the two global matrices guarantees the commutation of the corresponding matrices in each fragment. Therefore, many highly efficient numerical techniques such as the direct inversion of the iterative subspace method can be employed to converge simultaneously the electronic structure of all fragments, reducing significantly the computational cost. Numerical examples for water clusters of different sizes suggest that the method shall be very useful in improving the scalability of fragment quantum chemistry methods. © 2015 Wiley Periodicals, Inc.     

The non-Markovian quantum master equation in the collective-mode representation: application to barrier crossing in the intermediate friction regime

The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.     

A numerical method for the determination of atom—atom scattering amplitudes from the measured differential cross sections

A numerical method is given for the determination of the scattering amplitude, hence all the phase shifts, from the differential cross section at fixed energy. To obtain the phase of the scattering amplitude, the unitarity equation of scattering theory is solved, using the (experimental) cross section as input information. A straightforward iterative approach diverges for atom—atom input data, thus an appropriately modified method of solution is introduced to overcome this difficulty. The method was applied to two test cases, in both of which calculated atom—atom cross sections were used as simulated input data. Convergence to the correct phase was obtained in both examples, starting in each case with a guess phase function that differed considerably from the true solution. Convergence cannot be obtained, however, from an extremely poor starting phase. This study shows that the scattering amplitude for atomic scattering at thermal energies can be determined systematically, without use of parametrized functions, if a sufficiently accurate experimental cross section is available. A subsequent article describes a quantum mechanical procedure whereby the interaction potential can be constructed from the determined scattering amplitude.     

Combined molecular mechanical and quantum mechanical potential study of a nucleophilic addition reaction in solution

The procedure of combined semiempirical quantum mechanical (AM1) and molecular mechanical potential⁷ was used to study the nucleophilic addition of hydroxide to formaldehyde in solution. The gas phase AM1 potential surface is approximately 26 kcal/mol more exothermic than the corresponding ab initio 6-31 + G* calculation results. The free energy profile for the reaction in solution was determined by means of molecular dynamic simulations. The resulting free energy of activation is approximately 5 kcal/mol. The difference of the free energy of solvation between the reactant and the product states is about 38 kcal/mol. As the reaction goes on, the number of hydrogen bonds formed by the hydroxide oxygen with the surrounding water molecules decreases, whereas the number of hydrogen bonds formed by the carbonyl oxygen increases. There is no significant change in the total number of hydrogen bonds between the solute and the solvent molecules, and the average number of these hydrogen bonds is between five and six during the entire reaction process. These results are consistent with previous studies using a model based on ad initio 6-31 + G* calculations in the gas phase. The reaction path in solution is different from the gas phase minimum energy reaction path. When the two reactants are at a large distance, the attack route of the hydroxide anion in solution is close to perpendicular to the formaldehyde plane, whereas in the gas phase the route is collinear with the carbonyl group. These results suggests that although AM1 does not yield accurate energies in the gas phase, valuable insights into the solvent effects can be obtained through computer simulations with this combined potential. This combined procedure could be applied to chemical reactions within macromolecules, in which a quantitative estimation of the effects of the environment would not be easily attainable by another technique. © 1994 by John Wiley & Sons, Inc.     

Generalized formulation of quantum and classical crystallography using Green's functions

Quantum crystallography is a methodology by which structural information about a crystalline material obtained from X‐ray crystallography is combined with quantum mechanical methods. The objective is to enhance the data obtained from the X‐ray diffraction experiment, which are related to the atomic structure of the crystal, and to predict the properties and efficacy of those chemical compounds from which the crystals are derived. One approach in quantum crystallography is to use a projector matrix with a normalized trace. In this approach, quantum mechanical parameters in the projector matrix are fit into crystallographic data. During this fitting, the properties of the projector matrix called idempotency and normalization are used. Throughout this implementation procedure, Clinton's iteration scheme has been used in addition to the least‐squares technique. The purpose of the present study is to generalize Clinton's iterative equations in quantum crystallography by means of single‐particle Green's functions with the aid of the equal atoms model in the theory of direct methods. Convergency characters of the novel iterative equations are discussed by the steepest descent procedure. Furthermore, whether the calculations are valid in nonorthogonal bases was also examined. The iteration schemes widely used in quantum crystallography have been generalized but, in addition, the generalized expressions relating to the phase determination procedure and the probabilities of the sign relations between the structure factors are obtained and discussed comprehensively. The phrase order of crystallography has been put forward as a new concept. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Direct estimation of an element of order matrix from 1H NMR spectra of strongly dipolar coupled spins

NMR spectra of molecules oriented in thermotropic liquid crystalline media provide information on the molecular structure and order. The spins are generally strongly dipolar coupled and the spectral analyses require the tedious and time consuming numerical iterative calculations. The present study demonstrates the application of multiple quantum spin state selective detection of single quantum transitions for mimicking the homonuclear decoupling and the direct estimation of an element of ordering matrix. This information is utilized to estimate the nearly accurate starting dipolar couplings for iterative calculations. The studies on the spectra of strongly dipolar coupled five and six interacting spin systems are reported. Copyright © 2009 John Wiley & Sons, Ltd.     

Parallel iterative reaction path optimization in ab initio quantum mechanical/molecular mechanical modeling of enzyme reactions

The determination of reaction paths for enzyme systems remains a great challenge for current computational methods. In this paper we present an efficient method for the determination of minimum energy reaction paths with the ab initio quantum mechanical/molecular mechanical approach. Our method is based on an adaptation of the path optimization procedure by Ayala and Schlegel for small molecules in gas phase, the iterative quantum mechanical/molecular mechanical (QM/MM) optimization method developed earlier in our laboratory and the introduction of a new metric defining the distance between different structures in the configuration space. In this method we represent the reaction path by a discrete set of structures. For each structure we partition the atoms into a core set that usually includes the QM subsystem and an environment set that usually includes the MM subsystem. These two sets are optimized iteratively: the core set is optimized to approximate the reaction path while the environment set is optimized to the corresponding energy minimum. In the optimization of the core set of atoms for the reaction path, we introduce a new metric to define the distances between the points on the reaction path, which excludes the soft degrees of freedom from the environment set and includes extra weights on coordinates describing chemical changes. Because the reaction path is represented by discrete structures and the optimization for each can be performed individually with very limited coupling, our method can be executed in a natural and efficient parallelization, with each processor handling one of the structures. We demonstrate the applicability and efficiency of our method by testing it on two systems previously studied by our group, triosephosphate isomerase and 4-oxalocrotonate tautomerase. In both cases the minimum energy paths for both enzymes agree with the previously reported paths.     

Control of nonadiabatic dissociation dynamics with the use of laser-induced wave packet interferences

Based on wave packet interferences induced by a stationary laser field, a simple way of controlling nonadiabatic dissociation dynamics is proposed. We treat a simple two-state model of diatomic molecules. In this model, there exist two dissociative potential energy curves which cross and are strongly coupled at an internuclear distance, and thus dissociations into one channel are predominant. We propose a control scheme to selectively dissociate a molecule into any favorite channel by choosing the laser frequency and intensity appropriately. The semiclassical estimation of desirable laser parameters can be performed easily by regarding the dissociation processes as nonadiabatic transitions between the Floquet states. The agreement between the semiclassical estimation and the quantum wave packet calculation is found to be satisfactory in the high frequency region (> or =1000 cm(-1)) where the Floquet state picture is valid. In the low frequency region (<1000 cm(-1)), on the other hand, there are discrepancies between them due to the invalidity of the Floquet picture and the dissociation probability is sensitive to the laser phase. This control scheme is applied to the predissociation dynamics of NaI, NaI-->Na+I.     

A rigorous full-dimensional quantum dynamics calculation of the vibrational energies of H3O-2

The vibrational energy levels of the H(3)O-(2) anion have been calculated using a rigorous quantum dynamics method based on an accurate ab initio potential energy surface. The eigenvalue problem is solved using the two-layer Lanczos iterative diagonalization algorithm in a mixed grid/nondirect product basis set, where the system Hamiltonian is expressed in a set of orthogonal polyspherical coordinates. The lowest 312 vibrational energy levels in each inversion symmetry, together with a comparison of fundamental frequencies with previous quantum dynamics calculations, are reported. Finally, a statistical analysis of nearest level spacing distribution is carried out, revealing a strongly chaotic nature.