Bond softening

Last updated

Bond softening is an effect of reducing the strength of a chemical bond by strong laser fields. To make this effect significant, the strength of the electric field in the laser light has to be comparable with the electric field the bonding electron "feels" from the nuclei of the molecule. Such fields are typically in the range of 1–10 V/Å, which corresponds to laser intensities 1013–1015 W/cm2. Nowadays, these intensities are routinely achievable from table-top Ti:Sapphire lasers.

Contents

Theory

Theoretical description of bond softening can be traced back to early work on dissociation of diatomic molecules in intense laser fields. [1] While the quantitative description of this process requires quantum mechanics, it can be understood qualitatively using quite simple models.

Figure 1: Two theoretical models of a molecule interacting with laser field. At low intensity (a) it is convenient to plot molecular energy curves and indicate photon transitions with vertical arrows. At high intensity (b) it is more appropriate to "dress" the molecular curves in photons and consider photon transitions at the curve crossings. Hydrogen molecular ion dressed in photons.png
Figure 1: Two theoretical models of a molecule interacting with laser field. At low intensity (a) it is convenient to plot molecular energy curves and indicate photon transitions with vertical arrows. At high intensity (b) it is more appropriate to "dress" the molecular curves in photons and consider photon transitions at the curve crossings.

Low-intensity description

Consider the simplest diatomic molecule, the H2+ ion. The ground state of this molecule is bonding and the first excited state is antibonding. This means that when we plot the potential energy of the molecule (i.e. the average electrostatic energy of the two protons and the electron plus the kinetic energy of the latter) as the function of proton-proton separation, the ground state has a minimum but the excited state is repulsive (see Fig. 1a). Normally, the molecule is in the ground state, in one of the lowest vibrational levels (marked by horizontal lines).

In the presence of light, the molecule may absorb a photon (violet arrow), provided its frequency matches the energy difference between the ground and the excited states. The excited state is unstable and the molecule dissociates within femtoseconds into hydrogen atom and a proton releasing kinetic energy (red arrow). This is the usual description of photon absorption, which works well at low intensity. At high intensity, however, the interaction of the light with the molecule is so strong that the potential energy curves become distorted. To take this distortion into account requires "dressing" the molecule in photons.

Dressing in photons at high intensity

At high laser intensity absorptions and stimulated emissions of photons are so frequent that the molecule cannot be regarded as a system separate from the laser field; the molecule is "dressed" in photons forming a single system. However, the number of photons in this system varies when photons are absorbed and emitted. Therefore, to plot the energy diagram of the dressed molecule, we need to repeat the energy curves at each number of photons. The number of photons is very large but only a few curve repetitions need to be considered in this very tall ladder, as shown in Fig. 1b.

In the dressed model, photon absorption (and emission) is no longer represented by vertical transitions. As the energy must be conserved, photon absorption occurs at the curve crossings. For example, if the molecule is in the ground electronic state with 1015 photons present, it can jump to the repulsive state absorbing a photon at the curve crossing (violet circle) and dissociate to the 1015-1 photon limit (red arrow). This "curve jumping" is in fact continuous and can be explained in terms of avoided crossings.

Figure 2: Distortion of molecular energy curves dressed in photons for increasing laser intensity. Curve crossings become anticrossings, which induces bond softening. The distorted curves have been calculated from undistorted ones in Matlab using Hamiltonian diagonalisation. Bond softening induced by intense laser field.png
Figure 2: Distortion of molecular energy curves dressed in photons for increasing laser intensity. Curve crossings become anticrossings, which induces bond softening. The distorted curves have been calculated from undistorted ones in Matlab using Hamiltonian diagonalisation.

Energy curve distortion

When strong laser field perturbs the molecule, its energy levels are no longer the same as in the absence of the field. To calculate the new energy levels, [3] the perturbation must be included as off-diagonal elements of the Hamiltonian, which has to be diagonalised. In consequence, the crossings turn into anticrossings and the higher the laser intensity, the larger the gap of the anticrossing as shown in Fig. 2. The molecule can dissociate along the lower branch of the anticrossings as indicated by the red arrows.

The top arrow represents one photon absorption, which is a continuous process. In the region of the anticrossing the molecule is in a superposition of the ground and the excited states, continuously exchanging energy with the laser field. As the internuclear separation increases, the molecule absorbs energy and the electronic wavefunction evolves to the antibonding state on the femtosecond timescale. The H2+ ion dissociates to the 1ω limit.

The bottom arrow represents a process initiated at the 3-photon gap. As the system passes through this gap, the 1-photon gap is wide open and the system slides along the top branch of the 1-photon anticrossing. The molecule dissociates to the 2ω limit via absorption of 3 photons followed by re-emission of 1 photon. (One-step even-photon absorptions and emissions are forbidden by the symmetry of the system.)

The anticrossing curves are adiabatic, i.e. they are accurate only for infinitely slow transitions. When the dissociation is fast and the gap is small, a diabatic transition may occur where the system ends up on the other branch of the anticrossing. The probability of such a transition is described by the Landau–Zener formula. When applied to the dissociation through the 3-photon gap, the formula gives a small probability of the H2+ molecular ion ending up in the 3ω dissociation limit without emitting any photons.

Experimental confirmation

The "bond softening" phrase was coined by Phil Bucksbaum in 1990 at the time of its experimental observation. [4] A Nd:YAG laser was used to generate intense pulses of about 80 ps duration at the second harmonic of 532 nm. In a vacuum chamber, the pulses were focused on molecular hydrogen under low pressure (about 10−6 mbar) inducing ionization and dissociation. The kinetic energy of protons was measured in a time-of-flight (TOF) spectrometer. The proton TOF spectra revealed three peaks of kinetic energy spaced by a half of the photon energy. As the neutral H atom was taking the other half of the photon energy, this was an unambiguous confirmation of the bond softening process leading to the 1ω, 2ω and 3ω dissociation limits. Such a process which absorbs more than the minimum number of photons is known as above-threshold dissociation. [5]

A comprehensive review [6] puts the mechanism of bond softening in a broader research context. Anticrossings of diatomic energy curves have many similarities to the conical intersections of energy surfaces in polyatomic molecules. [7]

Related Research Articles

<span class="mw-page-title-main">Ionization</span> Process by which atoms or molecules acquire charge by gaining or losing electrons

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

<span class="mw-page-title-main">Rotational spectroscopy</span> Spectroscopy of quantized rotational states of gases

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The rotational spectrum of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy where rotational, vibrational and electronic energy changes occur simultaneously.

<span class="mw-page-title-main">Photoionization</span> Ion formation via a photon interacting with a molecule or atom

Photoionization is the physical process in which an ion is formed from the interaction of a photon with an atom or molecule.

<span class="mw-page-title-main">Franck–Condon principle</span> Quantum chemistry rule regarding vibronic transitions

The Franck–Condon principle is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions. The principle states that during an electronic transition, a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly.

Photodissociation, photolysis, photodecomposition, or photofragmentation is a chemical reaction in which molecules of a chemical compound are broken down by photons. It is defined as the interaction of one or more photons with one target molecule.

Rydberg ionization spectroscopy is a spectroscopy technique in which multiple photons are absorbed by an atom causing the removal of an electron to form an ion.

Ultrafast laser spectroscopy is a spectroscopic technique that uses ultrashort pulse lasers for the study of dynamics on extremely short time scales. Different methods are used to examine the dynamics of charge carriers, atoms, and molecules. Many different procedures have been developed spanning different time scales and photon energy ranges; some common methods are listed below.

<span class="mw-page-title-main">Doppler cooling</span> Laser cooling technique

Doppler cooling is a mechanism that can be used to trap and slow the motion of atoms to cool a substance. The term is sometimes used synonymously with laser cooling, though laser cooling includes other techniques.

<span class="mw-page-title-main">Two-photon absorption</span> Simultaneous absorption of two photons by a molecule

In atomic physics, two-photon absorption, also called two-photon excitation or non-linear absorption, is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy, most commonly an excited electronic state. Absorption of two photons with different frequencies is called non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the square of the light intensity; thus it is a nonlinear optical process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with absorption cross section typically several orders of magnitude smaller than one-photon absorption cross section.

<span class="mw-page-title-main">Lyman–Werner photons</span>

A Lyman-Werner photon is an ultraviolet photon with a photon energy in the range of 11.2 to 13.6 eV, corresponding to the energy range in which the Lyman and Werner absorption bands of molecular hydrogen (H2) are found. A photon in this energy range, with a frequency that coincides with that of one of the lines in the Lyman or Werner bands, can be absorbed by H2, placing the molecule in an excited electronic state. Radiative decay (that is, decay into photons) from this excited state occurs rapidly, with roughly 15% of these decays occurring into the vibrational continuum of the molecule, resulting in its dissociation. This two-step photodissociation process, known as the Solomon process, is one of the main mechanisms by which molecular hydrogen is destroyed in the interstellar medium.

<span class="mw-page-title-main">Positronium hydride</span> Exotic molecule consisting of a hydrogen atom bound to a positronium atom

Positronium hydride, or hydrogen positride is an exotic molecule consisting of a hydrogen atom bound to an exotic atom of positronium. Its formula is PsH. It was predicted to exist in 1951 by A Ore, and subsequently studied theoretically, but was not observed until 1990. R. Pareja, R. Gonzalez from Madrid trapped positronium in hydrogen laden magnesia crystals. The trap was prepared by Yok Chen from the Oak Ridge National Laboratory. In this experiment the positrons were thermalized so that they were not traveling at high speed, and they then reacted with H− ions in the crystal. In 1992 it was created in an experiment done by David M. Schrader and F.M. Jacobsen and others at the Aarhus University in Denmark. The researchers made the positronium hydride molecules by firing intense bursts of positrons into methane, which has the highest density of hydrogen atoms. Upon slowing down, the positrons were captured by ordinary electrons to form positronium atoms which then reacted with hydrogen atoms from the methane.

Photofragment ion imaging or, more generally, Product Imaging is an experimental technique for making measurements of the velocity of product molecules or particles following a chemical reaction or the photodissociation of a parent molecule. The method uses a two-dimensional detector, usually a microchannel plate, to record the arrival positions of state-selected ions created by resonantly enhanced multi-photon ionization (REMPI). The first experiment using photofragment ion imaging was performed by David W Chandler and Paul L Houston in 1987 on the phototodissociation dynamics of methyl iodide (iodomethane, CH3I).

The dihydrogen cation or hydrogen molecular ion is a cation with formula H+
2. It consists of two hydrogen nuclei (protons) sharing a single electron. It is the simplest molecular ion.

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

<span class="mw-page-title-main">Above-threshold ionization</span> Ionization by more photons than are required

In atomic, molecular, and optical physics, above-threshold ionization (ATI) is a multi-photon effect where an atom is ionized with more than the energetically required number of photons. It was first observed in 1979 by Pierre Agostini and colleagues in xenon gas.

Xenon monochloride (XeCl) is an exciplex which is used in excimer lasers and excimer lamps emitting near ultraviolet light at 308 nm. It is most commonly used in medicine. Xenon monochloride was first synthesized in the 1960s. Its kinetic scheme is very complex and its state changes occur on a nanosecond timescale. In the gaseous state, at least two kinds of xenon monochloride are known: XeCl and Xe
2Cl, whereas complex aggregates form in the solid state in noble gas matrices. The excited state of xenon resembles halogens and it reacts with them to form excited molecular compounds.

Double ionization is a process of formation of doubly charged ions when laser radiation is exerted on neutral atoms or molecules. Double ionization is usually less probable than single-electron ionization. Two types of double ionization are distinguished: sequential and non-sequential.

Vibronic spectroscopy is a branch of molecular spectroscopy concerned with vibronic transitions: the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy. In the gas phase, vibronic transitions are accompanied by changes in rotational energy also.

<span class="mw-page-title-main">Philip H. Bucksbaum</span>

Philip H. Bucksbaum is an American atomic physicist, the Marguerite Blake Wilbur Professor in Natural Science in the Departments of Physics, Applied Physics, and Photon Science at Stanford University and the SLAC National Accelerator Laboratory. He also directs the Stanford PULSE Institute.

Bond hardening is a process of creating a new chemical bond by strong laser fields—an effect opposite to bond softening. However, it is not opposite in the sense that the bond becomes stronger, but in the sense that the molecule enters a state that is diametrically opposite to the bond-softened state. Such states require laser pulses of high intensity, in the range of 1013–1015 W/cm2, and they disappear once the pulse is gone.

References

  1. ↑ Bandrauk, André D.; Sink, Michael L. (1981). "Photodissociation in intense laser fields: Predissociation analogy". J. Chem. Phys. 74 (2): 1110. Bibcode:1981JChPh..74.1110B. doi:10.1063/1.441217.
  2. ↑ Sharp, T.E. (1971). "Potential-energy curves for molecular hydrogen and its ions". Atomic Data. 2: 119–169. Bibcode:1971AD......2..119S. doi:10.1016/s0092-640x(70)80007-9.
  3. ↑ Giusti-Suzor, A.; Mies, F.H.; DiMauro, L.F.; Charron, E.; Yang, B. (1995). "Topical review: Dynamics of H2+ in intense laser fields". J. Phys. B. 28 (3): 309–339. Bibcode:1995JPhB...28..309G. doi:10.1088/0953-4075/28/3/006.
  4. ↑ Bucksbaum, P.H.; Zavriyev, A.; Muller, H.G.; Schumacher, D.W. (1990). "Softening of the H2+ molecular bond in intense laser fields". Phys. Rev. Lett. 64 (16): 1883–1886. Bibcode:1990PhRvL..64.1883B. doi:10.1103/physrevlett.64.1883. PMID   10041519.
  5. ↑ Zavriyev, A.; Bucksbaum, P.H.; Squier, J.; Saline, F. (1993). "Light-Induced Vibrational Structure in H2+ and D2+ in Intense Laser Fields". Phys. Rev. Lett. 70 (8): 1077–1080. Bibcode:1993PhRvL..70.1077Z. doi:10.1103/PhysRevLett.70.1077. PMID   10054280.
  6. ↑ Sheehy, B.; DiMauro, L. F. (1996). "Atomic and Molecular Dynamics in Intense Optical Fields". Annu. Rev. Phys. Chem. 47: 463–494. Bibcode:1996ARPC...47..463S. doi:10.1146/annurev.physchem.47.1.463.
  7. ↑ Natan, Adi; Ware, Matthew R.; Prabhudesai, Vaibhav S.; Lev, Uri; Bruner, Barry D.; Heber, Oded; Bucksbaum, Philip H. (2016). "Observation of Quantum Interferences via Light-Induced Conical Intersections in Diatomic Molecules". Physical Review Letters. 116 (14): 143004. arXiv: 1511.05626 . Bibcode:2016PhRvL.116n3004N. doi:10.1103/PhysRevLett.116.143004. PMID   27104704. S2CID   1710720.>
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.