Adiabatic state preparation of correlated wave functions with nonlinear scheduling functions and broken-symmetry wave functions.

Adiabatic state preparation (ASP) can generate the correlated wave function by simulating the time evolution of wave function under the time-dependent Hamiltonian that interpolates the Fock operator and the full electronic Hamiltonian. However, ASP is inherently unsuitable for studying strongly correlated systems, and furthermore practical computational conditions for ASP are unknown. In quest for the suitable computational conditions for practical applications of ASP, we performed numerical simulations of ASP in the potential energy curves of N, BeH, and in the C quasi-reaction pathway of the Be atom insertion to the H molecule, examining the effect of nonlinear scheduling functions and the ASP with broken-symmetry wave functions with the S operator as the penalty term, contributing to practical applications of quantum computing to quantum chemistry.

Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory.

A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer.

Quantum Algorithm for Full Configuration Interaction Calculations without Controlled Time Evolutions.

A quantum phase estimation algorithm allows us to perform full configuration interaction (full-CI) calculations on quantum computers with polynomial costs against the system size under study, but it requires quantum simulation of the time evolution of the wave function conditional on an ancillary qubit, which makes the algorithm implementation on real quantum devices difficult. Here, we discuss an application of the Bayesian phase difference estimation algorithm that is free from controlled time evolution operations to the full-CI calculations.

Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps.

Quantum computers can perform full configuration interaction (full-CI) calculations by utilising the quantum phase estimation (QPE) algorithms including Bayesian phase estimation (BPE) and iterative quantum phase estimation (IQPE). In these quantum algorithms, the time evolution of wave functions for atoms and molecules is simulated conditionally with an ancillary qubit as the control, which make implementation to real quantum devices difficult. Also, most of the problems in chemistry discuss energy differences between two electronic states rather than total energies themselves, and thus direct calculations of energy gaps are promising for future applications of quantum computers to real chemistry problems.

Smallest Organic Tetracation in the Gas Phase: Stability of Multiply Charged Diiodoacetylene Produced in Intense Femtosecond Laser Fields.

Coulomb explosion imaging, which is the reconstruction of a molecular structure by measuring the three-dimensional momenta of atomic ions formed by a Coulomb explosion of multiply charged molecular cations (MMCs), has been utilized widely. In contrast, intact MMCs, whose properties and reactions are interesting from both fundamental and applied scientific perspectives, themselves have been little explored to date. This study demonstrates that the four-atom molecule diiodoacetylene (DIA) can survive as a long-lived species in the gas phase after the removal of four electrons in intense femtosecond laser fields.

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions.

The Heisenberg exchange coupling parameter ( = -2 · ) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the value directly, without calculating the energies of individual spin states.

Quantum Algorithm for the Direct Calculations of Vertical Ionization Energies.

Recently, a quantum algorithm that is capable of directly calculating the energy gap between two electronic states having different spin quantum numbers without inspecting the total energy of the individual electronic states was proposed. This quantum algorithm guarantees an exponential speedup, like quantum phase estimation (QPE)-based full-CI, with much lower costs. In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates, extending the quantum algorithm to the direct calculation of vertical ionization energies.

A probabilistic spin annihilation method for quantum chemical calculations on quantum computers.

A probabilistic spin annihilation method based on the quantum phase estimation algorithm is presented for quantum chemical calculations on quantum computers. This approach can eliminate more than one spin component from the spin contaminated wave functions by single operation. Comparison with the spin annihilation operation on classical computers is given.

Trityl-Aryl-Nitroxide-Based Genuinely -Engineered Biradicals, As Studied by Dynamic Nuclear Polarization, Multifrequency ESR/ENDOR, Arbitrary Wave Generator Pulse Microwave Waveform Spectroscopy, and Quantum Chemical Calculations.

Trityl and nitroxide radicals are connected by π-topologically controlled aryl linkers, generating genuinely -engineered biradicals. They serve as a typical model for biradicals in which the exchange () and hyperfine interactions compete with the -difference electronic Zeeman interactions. The magnetic properties underlying the biradical spin Hamiltonian for solution, including 's, have been determined by multifrequency CW-ESR and H ENDOR spectroscopy and compared with those obtained by quantum chemical calculations.

Quantum chemistry on quantum computers: quantum simulations of the time evolution of wave functions under the S operator and determination of the spin quantum number S.

Quantum computers have an enormous impact on quantum chemical calculations. Approaches to calculate the energies of atoms and molecules on quantum computers by utilizing quantum phase estimation (QPE) and the variational quantum eigensolver (VQE) have been well documented, and dozens of methodological improvements to decrease computational costs and to mitigate errors have been reported until recently. However, the possible methodological implementation of observables on quantum computers such as calculating the spin quantum numbers of arbitrary wave functions, which is a crucial issue in quantum chemistry, has been discussed less.

Quantum Chemistry on Quantum Computers: A Method for Preparation of Multiconfigurational Wave Functions on Quantum Computers without Performing Post-Hartree-Fock Calculations.

The full configuration interaction (full-CI) method is capable of providing the numerically best wave functions and energies of atoms and molecules within basis sets being used, although it is intractable for classical computers. Quantum computers can perform full-CI calculations in polynomial time against the system size by adopting a quantum phase estimation algorithm (QPEA). In the QPEA, the preparation of initial guess wave functions having sufficiently large overlap with the exact wave function is recommended.

ESR analyses of picket fence Mn and 6th ligand coordinated Fe porphyrins (S = 5/2) and a Co(hfac) complex (S = 3/2) with sizable ZFS parameters revisited: a full spin Hamiltonian approach and quantum chemical calculations.

The fictitious spin-1/2 (effective spin-1/2) Hamiltonian approach has been the putative method to analyze the conventional fine-structure/hyperfine ESR spectra of high spin metallocomplexes with sizable zero-field splitting (ZFS) tensors since the early 1950s, and the approach gives salient principal geff-values far from g = 2 without explicitly affording their ZFS values in most cases. The experimental geff-values thus determined, however, never agree with those (gtrue-values) of the true principal g-tensors, which are obtainable from reliable quantum chemical calculations. We have recently derived exact or extremely accurate analytical expressions for the geff/gtrue relationships for the spin quantum number S's up to S = 7/2 (T.

Behaviour of DFT-based approaches to the spin-orbit term of zero-field splitting tensors: a case study of metallocomplexes, M(acac) (M = V, Cr, Mn, Fe and Mo).

Spin-orbit contributions to the zero-field splitting (ZFS) tensor (D tensor) of M(acac) complexes (M = V, Cr, Mn, Fe and Mo; acac = acetylacetonate anion) are evaluated by means of ab initio (a hybrid CASSCF/MRMP2) and DFT (Pederson-Khanna (PK) and natural orbital-based Pederson-Khanna (NOB-PK)) methods, focusing on the behaviour of DFT-based approaches to the D tensors against the valence d-electron configurations of the transition metal ions in octahedral coordination. Both the DFT-based approaches reproduce trends in the D tensors. Significantly, the differences between the theoretical and experimental D (D = D - (D + D)/2) values are smaller in NOB-PK than in PK, emphasising the usefulness of the natural orbital-based approach to the D tensor calculations of transition metal ion complexes.

Analyses of sizable ZFS and magnetic tensors of high spin metallocomplexes.

The fictitious spin-1/2 Hamiltonian approach is the putative method to analyze the fine-structure/hyperfine ESR spectra of high spin metallocomplexes having sizable zerofield splitting (ZFS), thus giving salient principal g-values far from around g = 2 without explicitly providing their ZFS parameters in most cases. Indeed, the significant departure of the g-values from g = 2 is indicative of the occurrence of their high spin states, but naturally they never agree with true g-values acquired by quantum chemical calculations such as sophisticated DFT or ab initio MO calculations. In this work, we propose facile approaches to determine the magnetic tensors of high spin metallocomplexes having sizable ZFS, instead of performing advanced high-field/high-frequency ESR spectroscopy.

Quasi-Restricted Orbital Treatment for the Density Functional Theory Calculations of the Spin-Orbit Term of Zero-Field Splitting Tensors.

A quasi-restricted orbital (QRO) approach for the calculation of the spin-orbit term of zero-field splitting tensors (D tensors) by means of density functional theory (DFT) importantly features in the fact that it is free from spin contamination problems because it uses spin eigenfunctions for the zeroth order wave functions. In 2011, however, Schmitt and co-workers pointed out that in the originally proposed QRO working equation some possible excitations were not included in their sum-over-states procedure, which causes spurious D contributions from closed-shell subsystems located far from the magnetic molecule under study. We have revisited the derivation of the QRO working equation and modified it, making it include all possible types of excitations in the sum-over-states procedure.

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum.

Intact Four-atom Organic Tetracation Stabilized by Charge Localization in the Gas Phase.

Several features distinguish intact multiply charged molecular cations (MMCs) from other species such as monocations and polycations: high potential energy, high electron affinity, a high density of electronic states with various spin multiplicities, and charge-dependent reactions. However, repulsive Coulombic interactions make MMCs quite unstable, and hence small organic MMCs are currently not readily available. Herein, we report that the isolated four-atom molecule diiodoacetylene survives after the removal of four electrons via tunneling.

Adiabatic quantum computing with spin qubits hosted by molecules.

A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs.

An ab initio MO study of heavy atom effects on the zero-field splitting tensors of high-spin nitrenes: how the spin-orbit contributions are affected.

The CASSCF and the hybrid CASSCF-MRMP2 methods are applied to the calculations of spin-spin and spin-orbit contributions to the zero-field splitting tensors (D tensors) of the halogen-substituted spin-septet 2,4,6-trinitrenopyridines, focusing on the heavy atom effects on the spin-orbit term of the D tensors (D(SO) tensors). The calculations reproduced experimentally determined |D| values within an error of 15%. Halogen substitutions at the 3,5-positions are less influential in the spin-spin dipolar (D(SS)) term of 2,4,6-trinitrenopyridines, although the D(SO) terms are strongly affected by the introduction of heavier halogens.

A new series of bis(ene-1,2-dithiolato)tungsten(IV), -(V), -(VI) complexes as reaction centre models of tungsten enzymes: preparation, crystal structures and spectroscopic properties.

The carbomethoxy substituted dithiolene ligand (L(COOMe)) enabled us to develop a series of new bis(ene-1,2-dithiolato)tungsten complexes including W(IV)O, W(IV)(OSiBuPh(2)), W(VI)O(2), W(VI)O(OSiBuPh(2)) and W(VI)O(S) core structures. By using these tungsten complexes, a systematic study of the terminal monodentate ligand effects has been performed on the structural, spectroscopic properties and reactivity. The structure and spectroscopic properties of the tungsten complexes have also been compared to those of the molybdenum complexes coordinated by the same ligand to investigate the effects of the metal ion (W vs.

Oxo-sulfido- and oxo-selenido-molybdenum(VI) complexes possessing a dithiolene ligand related to the active sites of hydroxylases of molybdoenzymes: low temperature preparation and characterisation.

Oxo-sulfido- and oxo-selenido-molybdenum(VI) complexes with an ene-1,2-dithiolate ligand are generated as models of the active sites of molybdenum hydroxylases. The sulfide and selenide groups are highly reactive toward triphenylphosphine in the order of Se > S.

Time-resolved electron paramagnetic resonance and phosphorescence studies of the lowest excited triplet states of Rh(III) corrole complexes.

The lowest excited triplet (T(1)) ππ* states of gallium (Ga) and various rhodium (Rh) 5,10,15-trispentafluorophenyl corroles (Cors) were studied in the liquid crystal (LC) E-7 and in rigid glasses by time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy. The triplet sublevel energies were experimentally determined by the alignment of the molecules in the LC and by magnetophotoselection in the glass. The sublevel scheme of GaCor was determined by calculating the zero field splitting (ZFS) parameters.

A synthetic two-spin quantum bit: g-engineered exchange-coupled biradical designed for controlled-NOT gate operations.

A quantum gate: A system of two coupled electron spins that is useful for simple quantum computing operations has been prepared by synthesis of a biradical 1 and co-crystallization with an isomorphous host molecule. The two weakly exchange-coupled quantum bits (target qubit blue and control qubit red) span four electron spin states. The electron spin transition is denoted by two black arrows.

Pulsed electron spin nutation spectroscopy of weakly exchange-coupled biradicals: a general theoretical approach and determination of the spin dipolar interaction.

Weakly exchange-coupled biradicals have attracted much attention in terms of their DNP application in NMR spectroscopy for biological systems or the use of synthetic electron-spin qubits. Pulse-ESR based electron spin nutation (ESN) spectroscopy applied to biradicals is generally treated as transition moment spectroscopy from the theoretical side, illustrating that it is a powerful and facile tool to determine relatively short distances between weakly exchange-coupled electron spins. The nutation frequency as a function of the microwave irradiation strength ω(1) (angular frequency) for any cases of weakly exchange-coupled systems can be classified into three categories; D(12) (spin dipolar interaction)-driven, Δg-driven and ω(1)-driven nutation behaviour with the increasing strength of ω(1).