Probability Amplitude Of State Research Articles

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4.

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

An Efficient Approach for Studies of Water Clusters Using Diffusion Monte Carlo.

An efficient and accurate approach for using diffusion Monte Carlo (DMC) to study molecular clusters is described and applied to an investigation of (H2O)n with n = 1, 2, 3. In this approach, importance sampled DMC is used to describe the intramolecular degrees of freedom of the water monomers. The intermolecular degrees of freedom are treated using standard unguided DMC approaches. This hybrid approach allows us to use significantly smaller simulations to obtain converged zero-point energies and ground state wave functions than would be required for a fully unguided simulation of the same system. We demonstrate the efficiency, accuracy, and utility of this approach through a study of nine isotopologues of water trimer, focusing on how the ground state probability amplitude for these clusters samples the various low-energy minima on the potential surface.

Statistical Analysis of the Effect of Deuteration on Quantum Delocalization in CH5.

Statistical approaches are applied to an investigation of how deuterated forms of CH5+ sample the potential energy surface for this ion. In its ground state, CH5+ has been shown to have amplitude in all of the 120 equivalent minima in the potential as well as in the region of each of the 180 low-energy saddle points that connect these minima. Although deuteration quenches this delocalization, the multidimensional nature of the isomerization pathways makes it difficult to visualize and quantify the delocalization of the ground state wave function. In this work, the localization of the ground state wave function is explored through an analysis of projections of the ground state probability amplitude onto various atom-atom distances. Specifically, analysis of two-dimensional projections of the ground state probability amplitude on to the distances between pairs of hydrogen atoms reveals that the ground state probability amplitude is localized near structures in which the hydrogen atoms in the ion can be divided into those that make up a CH3+ part and those that make up in a H2 part. Analysis of fits of projections of the probability amplitude onto distances between pairs of hydrogen atoms, between pairs of deuterium atoms, and between hydrogen and deuterium atoms to sums of Gaussian functions allows us to quantify the increased localization of hydrogen and deuterium atoms in the CH3+ and H2 parts of the ion. In addition, the amplitude of the wave function in the regions of the potential that correspond to the transition state for exchange of hydrogen or deuterium atoms between these two parts of the ion is found to decrease in the partially deuterated forms of CH5+ and is smallest for CH2D3+ and CH3D2+.

Tag-Free and Isotopomer-Selective Vibrational Spectroscopy of the Cryogenically Cooled H9O4+ Cation with Two-Color, IR-IR Double-Resonance Photoexcitation: Isolating the Spectral Signature of a Single OH Group in the Hydronium Ion Core.

We report vibrational spectra of the cryogenically cooled H9O4+ cation along with those of the D2 tagged HD8O4+ isotopomers using two variations on a two-color, IR-IR double-resonance photoexcitation scheme. The spectrum of the isolated H9O4+ ion consists of two sharp features in the OH stretching region that indicate exclusive formation of the "Eigen" cation, the H3O+·(H2O)3 isomer that corresponds to the filled hydration shell around the hydronium ion. Consistent with this structural assignment, the spectrum of the HD8O4+ isotopologue is resolved into contributions from two isotopomers: one with the single OH group on one of the three solvent water molecules and another in which it resides on the hydronium core ion. The latter spectrum is dominated by a broad feature assigned to the isolated hydronium OH stretching fundamental with an envelope that is similar to that displayed by the H3O+·(H2O)3 isotopologue. The feature appears with a diffuse band ∼380 cm-1 above it, which is assigned to a combination band involving the hydronium OH stretching vibration and the frustrated translation mode of the HD2O+ core and one of the solvating water molecules. These trends are analyzed with anharmonic calculations involving four-mode coupling on a realistic potential surface and interpreted in the context of vibrationally adiabatic potentials based on insights acquired from analysis of the ground state probability amplitudes obtained from diffusion Monte Carlo calculations.

Quantum-Inspired Neural Network with Sequence Input

To enhance the approximation and generalization ability of artificial neural network (ANN) by employing the principles of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-not gate after being rotated by the quantum rotation gates, control the target qubit for reverse. The model output is described by the probability amplitude of state in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the sequence input-based quantum-inspired neurons to the hidden layer and the classical neurons to the output layer, and a learning algorithm is derived by employing the Levenberg-Marquardt algorithm. Simulation results of benchmark problem show that, under a certain condition, the QNNSI is obviously superior to the ANN.

Microwave Effect in Chemical Reactions

Microwave Effect in Chemical Reactions Samuel P. Bowen, David R. Kanis, Christopher McDaniel, Robert C Richter Abstract Time dependent perturbation theory predicts no change in the electronic state probability amplitudes of molecules unless the energy of the applied electromagnetic field matches an electronic energy level difference. Therefore, microwaves should have no non-thermal effect on chemical reactions. However, at low frequencies the oscillating potentials are essentially classical and the relevant question is whether the electronic molecular states evolve adiabatically or non-adiabatically. Time varying potentials can mix excited states into the instantaneous adiabatic ground state as the expectation of the energy changes in response to the potential. This mixing yields a non-zero excited state proba bi l i t y a mp l i t u d e s c n (t). Measurements of these excited states, for example, by reactant collisions, may collapse the instantaneous ground state wave function onto the excited state with a probability |cn (t)|2. This nonadiabatic probability o pe ns a new channel for chemical reactions in addition to the usual thermal Ar r h e n i u s probability. The temperature dependence of the reaction rate from these two channels will exhibit the microwave effects primarily at low temperatures. At high temperatures the Arrhenius probabili ti es wi l l dominate and the microwave effects may be negligible. Most precise laboratory a s s e s s me n t s of non-thermal mi crowave effects appear to have been at high temperatures. Several experiments are reviewed and one is found to have a wide enough temperature range to exhibit the predicted f o rm. Our results also suggest that m i c r o w a v e couplings could induce reactions different from those weighted by the thermal probabilities. Full Text: PDF DOI: 10.15640/jcb.v2n2a1

Sequence Input-Based Quantum-Inspired Neural Networks with Applications

To enhance the approximation and generalization ability of artificial neural networks (ANNs) by employing the principle of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-not gate after being rotated by the quantum rotation gates, control the target qubit for reverse. The model output is described by the probability amplitude of state $$|1\rangle $$ | 1 ? in the target qubit. Then a quantum-inspired neural networks (QINN) is designed by employing the quantum-inspired neurons to the hidden layer and the common neurons to the output layer. The algorithm of QINN is derived by employing the Levenberg---Marquardt algorithm. Simulation results of some benchmark problems show that, under a certain condition, the QINN is obviously superior to the classical ANN.

Model and algorithm of quantum-inspired neural network with sequence input based on controlled rotation gates

To enhance the approximation and generalization ability of classical artificial neural network (ANN) by employing the principles of quantum computation, a quantum-inspired neuron based on controlled-rotation gate is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-rotation gate after being rotated by the quantum rotation gates, control the target qubit for rotation. The model output is described by the probability amplitude of state |1〉 in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the quantum-inspired neurons to the hidden layer and the classical neurons to the output layer. An algorithm of QNNSI is derived by employing the Levenberg–Marquardt algorithm. Experimental results of some benchmark problems show that, under a certain condition, the QNNSI is obviously superior to the ANN.

Investigation of the Structure and Spectroscopy of H5+ Using Diffusion Monte Carlo

The results of diffusion Monte Carlo (DMC) calculations of the ground and selected excited states of H5(+) and its deuterated analogues are presented. Comparisons are made between the results obtained from two recently reported potential surfaces. Both of these surfaces are based on CCSD(T) electronic energies, but the fits display substantial differences in the energies of low-lying stationary points. Little sensitivity to these features is found in the DMC results, which yield zero-point energies based on the two surfaces that differ by between 20 and 30 cm(–1) for all twelve isotopologues of H5(+). Likewise, projections of the ground state probability amplitudes, evaluated for the two surfaces, are virtually identical. By using the ground state probability amplitudes, vibrationally averaged rotational constants and dipole moments were calculated. On the basis of these calculations, all isotopologues are shown to be near-prolate symmetric tops. Further, in cases where the ion had a nonzero dipole moment, the magnitude of the vibrationally averaged dipole moment was found to range from 0.33 to 1.15 D, which is comparable to the dipole moments of H2D+ and HD2(+). Excited states with up to three quanta in the shared proton stretch and one quantum in the in-phase stretch of the outer H2 groups were also investigated. Trends in the energies and the properties of these states are discussed.

Quantum process neural networks model algorithm and applications

To enhance the approximation and generalization ability of process neural networks (PNNs), by studying the quantum implementation mechanism of information processing of process neuron, a new idea of designing quantum process neuron is proposed in this paper, based on the quantum rotation gates and the quantum controlled-non gates. In the proposed approach, the discrete process inputs are expressed by the qubits, which, as the control qubits of controlled-non gates after being rotated by the quantum rotation gates, control the target qubits to reverse. The model outputs are described by the probability amplitude of state |1 in the target qubits. Then the quantum process neural networks (QPNNs) are designed by the quantum process neurons for the hidden layer and the normal neurons for the output layer. The algorithm of QPNN is derived through the quantum computing. The proposed approach is utilized to predict the smoothed yearly mean sunspot numbers, and the results indicate that the QPNN has higher prediction accuracy than the normal PNN, thus it has a certain theoretical meaning and practical value for the complex prediction.

Unraveling Anharmonic Effects in the Vibrational Predissociation Spectra of H5O2+ and Its Deuterated Analogues

The nature of anharmonic couplings in the H(5)O(2)(+) "Zundel" ion and its deuterated isotopologues is investigated through comparison of their measured and calculated vibrational spectra. This follows a recent study in which we reported spectra for H(5)O(2)(+), D(5)O(2)(+), and D(4)HO(2)(+) from ∼600 to 4000 cm(-1), as well as H(4)DO(2)(+) in the OH and OD stretching regions [ J. Phys. Chem. B 2008 , 112 , 321 ]. While the assignments of the higher-energy transitions associated with the fundamentals of the exterior OH and OD motions are relatively straightforward, difficulties arise in the assignment of the lower-frequency regions that involve displacement of the bridging proton, especially for the isotopically mixed species. Here we revisit the Ar-tagged isotopomers, and report the low energy action spectrum of H(4)DO(2)(+) for the first time, as well as present significantly improved spectra for the D(4)HO(2)(+) and D(5)O(2)(+) systems. Band assignments are clarified in several cases using IR-IR hole-burning. We then investigate the physical origin of the anharmonic effects encoded in these spectra using a recently developed technique in which the anharmonic frequencies and intensities of transitions (involving up to two quanta of excitation) are evaluated using the ground state probability amplitudes [ J. Phys. Chem. A 2009 , 113 , 7346 ] obtained from diffusion Monte Carlo simulations. This approach has the advantage that it is applicable to low-symmetry systems [such as (HDO)H(+)(OH(2))] that are not readily addressed using highly accurate methods such as the multiconfigurational time-dependent Hartree (MCTDH) approach. Moreover, it naturally accommodates an intuitive evaluation of the types of motion that contribute oscillator strength in the various regions of the spectrum, even when the wave function is intrinsically not separable as a product of low-dimensional approximate solutions. Spectra for H(5)O(2)(+), D(5)O(2)(+), H(4)DO(2)(+), and D(4)HO(2)(+) that are calculated by this approach are shown to be in excellent agreement with the measured spectra for these species, leading to reassignments of two of the bands in the intramolecular bending region of D(4)HO(2)(+).

Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology

The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal, et al., J. Opt. Soc. Am. B, 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled N00N state (|2,0>+|0,2>)/sqrt{2}. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. The output contains a family of entangled states directly applicable to quantum key distribution. Specific output states allow for the heralded creation of N=4 N00N states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity.

Chirping a two-photon transition in a multistate ladder

We consider a two-photon transition in a specific ladder system driven by a chirped laser pulse. In the weak field limit, we find that the excited state probability amplitude arises due to interference of multiple quantum paths which are weighted by quadratic phase factors. The excited state population has the form of a Gauss sum which plays a prominent role in number theory.

Multiband theory of Bloch electron dynamics in electric fields

A novel multiband theory of Bloch electron dynamics in homogeneous electric fields of arbitrary strength and time dependence is presented. In this formalism, the electric field is described through the use of the vector potential. Multiband coupling is treated through the use of the Wigner-Weisskopf approximation, thus allowing for a Bloch electron transition out of the initial band due to the power absorbed by the electric field; also, the approximation ensures conservation of the total transition probability over the complete set of excited bands. The choice of the vector potential gauge leads to a natural set of extended time-dependent basis functions for describing Bloch electron dynamics in a homogeneous electric field; an associated basis set of localized, electric-field-dependent Wannier and related envelope functions are developed and utilized in the analysis to demonstrate the inherent localization manifest in Bloch dynamics in the presence of relatively strong electric fields. From the theory, a generalized Zener tunnelling time is derived in terms of the applied uniform electric field and the relevant band parameters. The analysis shows an electric-field-enhanced broadening of the excited state probability amplitudes, thus resulting in spatial lattice delocalization and the onset of smearing of discrete, Stark ladder and band-to-band transitions due to the presence of the electric field. In addition, the velocities of a Bloch oscillation will be observed only for the electron that is initially in a Bloch state before Zener tunnelling. Further, the influence of electric fields on resonant tunnelling structure is examined.