Diatomic Research Articles

Extended improved multiparameter exponential‐type potential energy function for diatomic molecules

AbstractBased on the improved multiparameter exponential‐type potential (IMPET), an extended IMPET (EIMPET) potential has been suggested to reduce the discrepancy between the calculated and experimental values, improving the accuracy near the equilibrium and in the asymptotic region. The average fitting deviation δav and Root‐Mean‐Square (RMS) error is used to evaluate the performance of the potential which generates potential energy curves (PECs) and vibrational energy levels for ClF‐A(3Π1), CP‐X2Σ+, ICl‐X1Σ+, IBr‐X1Σ+, CO‐X1Σ+, and 6Li2‐X1Σ+ molecules that agree better with the Rydberg‐Klein‐Rees (RKR) data than Morse, Huxley‐Murrell (HM) and IMPET potentials. This work provides a reference for the construction and improvement of potential energy functions for diatomic molecules.

Multiple Bonding in AeN- (Ae = Ca, Sr, Ba).

Quantum chemical calculations using ab initio methods at the MRCI+Q(8,9)/def2-QZVPPD and CCSD(T)/def2-QZVPPD levels as well as density functional theory are reported for the diatomic molecules AeN- (Ae = Ca, Sr, Ba). The nature of the bonds is analyzed with a variety of methods. The anions CaN- and SrN- have electronic triplet (3Π) ground states with nearly identical bond dissociation energies De ~57 kcal/mol calculated at the MRCI+Q(8,9)/def2-QZVPPD level of theory. In contrast, the heavier homologue BaN- has a singlet (1Σ+) ground state, which is only 1.1 kcal/mol below the triplet (3Σ-) state. The computed bond dissociation energy of (1Σ+) BaN- is 68.4 kcal/mol. The calculations at the CCSD(T)-full/def2-QZVPPD and BP86-D3(BJ)/def2-QZVPPD levels of theory are in reasonable agreement with the MRCI+Q(8,9)/def2-QZVPPD data except for the singlet (1Σ+) state, which has a large multireference character. The calculated atomic partial charges given by the CM5, Voronoi and Hirshfeld methods suggest small to medium-sized charge donation toward Ae atom Ae←N- for most electronic states. In contrast, the NBO method predicts for all species medium to large electronic charge donation toward nitrogen Ae→N-, which is due to the neglect of the (n)p AOs of Ae atoms as genuine valence orbitals.

Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities.

It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.

Reasons Why Most Single-Reference Coupled Cluster Methods Fail to Provide the Correct Adiabatic Potentials of a Diatomic Carbon Molecule: UCCSDecCCSD Potential Study.

Many single-reference coupled cluster (CC) methods offer adiabatically incorrect potentials when calculating the diatomic carbon molecule, so this problem has been studied extensively. Analysis of the full configuration interaction (FCI) wave function indicates that the main cause of the adiabatic collapse of potentials calculated by the CC method with singles, doubles, and triples (CCSDT) is the strongly increasing bonding character of the T4FCI cluster contribution. In turn, comparative analysis of the CCSDTQ adiabats X1Σg+ and B'1Σg+ demonstrates that the gap between them near the avoided crossing geometry is significantly reduced by quantitatively differentiating the character of the T4 and cluster contributions. These observations clearly indicate the need to take into account the T4 cluster contribution in the standard CC wave function to obtain the correct adiabatic potential. Further analysis of this issue shows that the T4 contribution must be additionally bonding to ensure the adiabatic correctness of the potential. What also seems very interesting is that when the UCCSDecCCSD method [Toboła, Chem. Phys. Lett. 2014, 614, 82-88] is used for the potential calculation, the shape of the potential is entirely determined by a subset of unrestricted Hartree-Fock (UHF) configurations, which are structurally identical to the ground-state configuration in the UHF-based CCSD wave function.

Classical and quantum light-induced non-adiabaticity in molecular systems

The exchange of energy between electronic and nuclear motion is the origin of non-adiabaticity and plays an important role in many molecular phenomena and processes. Conical intersections (CIs) of different electronic potential energy surfaces lead to the most singular non-adiabaticity and have been intensely investigated. The coupling of light and matter induces conical intersections, which are termed light-induced conical intersections (LICIs). There are two kinds of LICIs, those induced by classical (laser) light and those by quantum light like that provided by a cavity. The present work reviews the subject of LICIs, discussing the achievements made so far. Particular attention is paid to comparing classical and quantum LICIs, their similarities and differences and their relationship to naturally occurring CIs. In contrast to natural CIs, the properties of which are dictated by nature, the properties of their light-induced counterparts are controllable by choosing the frequency and intensity (or coupling to the cavity) of the external light source. This opens the door to inducing and manipulating various kinds of non-adiabatic effects. Several examples of diatomic and polyatomic molecules are presented covering both dynamics and spectroscopy. The computational methods employed are discussed as well. To our opinion, the young field of LICIs and their impact shows much future potential.

ENERGY SPECTRA, EXPECTATION VALUES, AND THERMODYNAMIC PROPERTIES OF HCl AND LiH DIATOMIC MOLECULES

The Schrödinger equation is solved by applying the Nikiforov-Uvarov-Functional Analysis method to the Hulthén plus screened Kratzer Potential. The Greene-Aldrich approximation is employed to determine the closed form expressions for the energy equation and the wave function. The Hellmann-Feynman theorem was employed to calculate the energy spectra and expectation values of various quantum states for diatomic moleculesof HCl and LiH. Subsequently, we employed the energy equation that we had previously derived to compute the partition function, which in turn enabled us to determine the thermodynamic properties associated with the diatomic molecules. The partition function for the diatomic molecules of 2Hand LiHwas calculated at different temperatures. The results indicate that the partition function of the two diatomic molecules rose as the temperature increased.The findings we obtained align with the results documented in the literature.

Spectroscopic Identification and Photochemistry of Astrochemically Relevant Phosphorus-bearing Molecules [O, C, N, P] and [2O, C, N, P]

Diatomic molecules phosphorus monoxide (PO) and phosphorus mononitride (PN) are the main reservoirs of gas-phase phosphorus in interstellar and circumstellar environments, indicating the possibility of forming new phosphorus-bearing molecules through reactions with other interstellar species. To explore the astrochemistry of PO and PN, new simple phosphorus-bearing molecules [O, C, N, P] and [2O, C, N, P] were generated in the gas phase and isolated in cryogenic matrices for characterization with matrix-isolation IR and UV/vis spectroscopy in combination with calculations at the CCSD(T)-F12a/VTZ-F12 level of theory. In an inert argon matrix, OPCN isomerizes to OPNC upon UV-light irradiation at 365 nm, followed by successive isomerizations to PNCO and POCN with concomitant dissociation to diatomic PN and CO under further irradiation at 193 nm. By analogy, the isomerization of O2PCN to O2PNC and OPNCO followed by fragmentation to OPN/CO and PN/CO2 occurs in the matrix upon irradiation at 193 nm. In a chemically active CO ice, the photolytic reaction of OPCN with CO yields CO2 and PCN, and O2PCN reacts with CO by forming OPCN and CO2, in which the photochemical networks for these P-bearing species linking the astrochemically important PN and PO have been proposed. The experimental identification of these phosphorus-bearing molecules is supported by quantum chemical calculations, and the spectroscopic data may aid in their detection in the interstellar and circumstellar medium.

Proton tunneling in the dissociation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses.

Light-induced deprotonation of molecules is an important process in photochemical reactions. Here, we theoretically investigate the tunneling deprotonation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses. The quasi-static picture shows that the field-dressed potential barrier is significantly lowered for the deprotonation channel when the mass asymmetry of the diatomic molecule increases. Our numerical simulations demonstrate that when the mass symmetry breaks, the tunneling deprotonation is significantly enhanced and the proton tunneling becomes the dominant dissociation channel in the THz driving fields. In addition, the simulated nuclear momentum distributions show that the emission of the proton is directed by the effective vector potential for the deprotonation channel and, meanwhile, the angular distribution of the emitting proton is affected by the alignment and rotation of the molecule induced by the rotating field.

Analyzing the photoassociation spectrum of ultracold 85Rb 133Cs molecule in (3)3Σ+ state.

We establish a theoretical model to analyze the photoassociative spectroscopy of 85Rb 133Cs molecules in the (3)3Σ+ state. The vibrational energy, spin-spin coupling constant, and hyperfine interaction constant of the (3)3Σ+ state are determined based on nine observed vibrational levels. Consequently, the Rydberg-Klein-Rees potential energy curve of the (3)3Σ+ state is obtained and compared with the ab initial potential energy curve. Our model can be adopted to analyze the photoassociative spectroscopy of other heteronuclear alkali-metal diatomic molecules in the (3)3Σ+ state.

Dynamics of an ultracold weakly bound heteronuclear diatomic molecule in an ultrashort laser pulse

Dynamics of an ultracold weakly bound heteronuclear diatomic molecule in an ultrashort laser pulse

Hydrogen-Bonded Complex of the Parent Phosphinidene.

The diatomic molecule PH is very reactive, and it serves as the parent compound for phosphinidenes featuring a monovalent phosphorus atom. Herein, we report the characterization and reactivity of a rare hydrogen-bonded complex of PH. Specifically, the molecular complex between PH and HCl has been generated by photolysis of chlorophosphine (H2 PCl) at 254 nm in a solid Ar-matrix at 10 K. The IR spectrum of the complex HP⋅⋅⋅HCl and quantum chemical calculations at the UCCSD(T)-F12a/haTZ level consistently prove that the phosphorus atom acts as a hydrogen bond acceptor with a binding energy (D0 ) of -0.6 kcal mol-1 . In line with the observed absorption at 341 nm for the binary complex, the triplet phosphinidene PH undergoes prototype H-Cl bond insertion by reformation of H2 PCl upon photoexcitation at 365 nm. However, this hydrogen-bonded complex is unstable in the presence of N2 and HCl, as both molecules prefers stronger interactions with HCl than PH in the observed complexes HP⋅⋅⋅HCl⋅⋅⋅N2 and HP⋅⋅⋅2HCl.

Floquet Engineering of a Diatomic Molecule through a Bichromatic Radiation Field.

We report on a theoretical study of a Cs2 molecule illuminated by two lasers and show how this can result in novel quantum dynamics. We reveal that these interactions facilitate the bypass of the non-crossing rule, forming light-induced conical intersections and modifiable avoided crossings. Our findings show how laser field orientation and strength, along with initial phase differences, can control molecular-state transitions, especially on the micromotion scale. We also extensively discuss how the interaction of radiation with matter gives rise to the emergence of potential energy surfaces of hybrids of radiation and molecular states. This research advances a technique for manipulating photoassociation processes in Cs2 molecules, offering potential new avenues in quantum control.

Electronic structure with spin-orbit coupling effect of HfH molecule for laser cooling investigations

The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ - Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.

Path Integral Treatment of a Linear Combination of Deformed Diatomic Molecule Potentials

Path Integral Treatment of a Linear Combination of Deformed Diatomic Molecule Potentials

Predissociation dynamics of D2 revealed by variation in fragment anisotropy parameters along the Fano profile.

We conducted a study on the variations of the fragment anisotropy parameters (β) along the Fano profiles for the predissociation of the D2molecule. These variations, known as β profiles, were measured for the D(2l) fragments from the predissociation of the 4pπD'Πu1υ'=1 and 4pσB″Σu+1υ'=2 states. The measured β profiles show significant asymmetry and broader linewidths compared to the corresponding Fano profiles. By fitting the β profiles, we were able to determine the fragment anisotropy parameters associated with the resonance state, continuum state, and the interference effect between them. Additionally, we determined the ratios of the absorption cross sections between the unperturbed and perturbed continuum states interacting with the resonance states although these ratios were found to be very small. Furthermore, we derived approximate formulas to calculate the parameters characterizing the β profile. Despite the linewidths of the four Fano profiles being narrower than our instrumental resolution, we were still able to determine the product of the linewidth with the Fano q parameters. These findings demonstrate the utility of the β profile as an effective tool for studying the predissociation dynamics in diatomic molecules.

Enthalpy, mean energy, entropy, and Gibbs free energy of lithium dimer under magnetic field

It is well known that the lithium diatomic molecule has important potential application in engineering, and industry. For this purpose, in this research, the thermal properties of the lithium diatomic molecule are theoretically calculated taking into account both an external magnetic field and Aharonov-Bohm (AB) flux. To this end, the interaction in the diatomic molecule is proposed as an improved Scarf ΙΙ potential model (ISPM). The Schrödinger equation is solved using an appropriate Pekeris-like approximation form for the centrifugal barrier and the energy spectrum and wave functions are obtained. Then, the partition function is obtained to study the thermal properties of the lithium dimer. The calculated thermal properties of 7Li2 (2 3Πg) in this work are mean energy, entropy, specific heat, enthalpy, and Gibbs free energy. Our theoretical results are also compared with the experimental data. The findings show that the obtained results are in good agreement with experimental data. Without considering the magnetic field and AB flux, the deviation of specific heat, Gibbs free energy, and enthalpy are 3.73%, 4.96%, and 5.31%, respectively. By considering the magnetic field and AB flux, we find that the deviation of the aforementioned properties are 1.91%, 2.04%, and 2.32%, respectively. Therefore, it is found that the external magnetic field and AB flux have great influences on the thermal properties of lithium.

Importance profiles. Visualization of atomic basis set requirements

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function |α⟩ centered on some nucleus can be visualized by projecting |α⟩ on the set of numerically represented occupied orbitals |ψi⟩ as I0(α)=∑i⟨α|ψi⟩⟨ψi|α⟩ . Choosing α to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visualization I0(α) has the important property 0⩽I0(α)⩽1 which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic applications I(α) , in which the importance of a test function |α⟩ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

Adsorption of cadmium selenide clusters: A novel approach to enhance solar energy conversion using armchair graphene nanoribbons

Tailoring the electronic, optical, and transport properties of low-dimensional semiconductor materials is essential to improve the light-conversion efficiency of thin-film solar cell materials. Here, using first-principles calculations and non-equilibrium Green functions, we investigate the enhancement of optoelectronic and transport properties of armchair graphene nanoribbons (AGNRs) upon adsorption of cadmium selenide clusters. Upon adsorption of a CdSe diatomic molecule on an AGNR, the most energetically favorable configuration is the cadmium end sitting on top of a carbon atom. The corresponding electronic bandgap reduces ∼5 times with respect to that of the pristine system, thanks to the formation of a polaron state formed by the p-orbital of the selenide atom. Upon adsorption of CdSe cyclohexane molecules, the bandgap of this system slightly shrinks by 0.121 eV with respect to the pristine system. The charge accumulation induced by these clusters significantly enhances the absorption coefficient of the adsorbed systems, resulting in a red shift of the optical spectra toward the infrared region. More interestingly, by solving the Bethe–Salpeter equations with the Tamm–Dancoff approximation, we provide a direct link between the first-principles optical prediction and experimental observations. In addition, the electron transfer from these molecules to the hosted systems increases the transmission spectra in the vicinity of the Fermi level, leading to a remarkable electronic current passing through these scattering regions. These results highlight the role of cadmium selenide clusters in enhancing the light-to-energy conversion efficiency of next-generation solar cell devices.

Non-relativistic energy equations for diatomic molecules constrained in a deformed hyperbolic potential function.

In this paper, the approximate analytical energy equations for the deformed hyperbolic potential have been obtained for arbitrary parameters of the potential. The potential function was transformed to a molecular potential by subjecting it to the Varshni conditions which allows for the determination of the energy levels of diatomic molecules. The molecular vibrational energy spectra for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] diatomic molecules were obtained and found to match with the results obtained with another analytical approach, potential functions, and experimental data. The noticeable slight differences in the approximate energy spectra obtained in this work and existing literature may be ascribed to the analytical method, computational approach, and the accuracy of the molecular potential functions. The obtained energy equations were used to determine the energy of a particle for arbitrary parameters of the potential function. The obtained energy is bounded and increases with the increase in the quantum numbers. The results conformed to the ones obtained via the path integral approach and numerical solutions obtained via the MATHEMATICA program. The energy spectra equations were obtained via the Nikiforov-Uvarov approach and semi-classical WKB approximation. The Pekeris approximation has been applied to resolve the difficulty in solving the complete energy spectrum of the non-relativistic wave equation for the potential function. The numerical data of the energy spectra was obtained using the MATHEMATICA program.

Implementation of the Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Diatomic Molecules.

We present a computational approach that implements the time-dependent complete-active-space self-consistent-field method, as introduced in [Phys. Rev. A 88, 023402 (2013)]. Our implementation addresses the challenge of diatomic molecules subjected to an intense laser pulse by considering the full dimensionality of the problem using prolate spheroidal coordinates. The method incorporates the gauge-invariant frozen-core approximation, boosts the evaluation of the electron-electron interaction term using finite-element discrete-variable representation with Neumann expansion, and utilizes an exponential time differencing scheme tailored for the stable propagation of the stiff nonlinear orbital functions. We have successfully applied this methodology to study high-harmonic generation in diatomic molecules such as H2, LiH, and N2, shedding light on the impact of electron correlations in these systems.