Second-order Perturbation Theory Research Articles

Toward the identification of cyano-astroCOMs via vibrational features: benzonitrile as a test case.

The James Webb Space Telescope (JWST) opened a new era for the identification of molecular systems in the interstellar medium (ISM) by vibrational features. One group of molecules of increasing interest is cyano-derivatives of aromatic organic molecules, which have already been identified in the ISM on the basis of the analysis of rotational signatures, and so, are plausible candidates for the detection by the JWST. Benzonitrile considered in this work represents a suitable example for the validation of a computational strategy, which can be further applied for different, larger, and not-yet observed molecules. For this purpose, anharmonic simulations of infrared (IR) spectra have been compared with recent FTIR experimental studies. The anharmonic computations using the generalized second-order vibrational perturbation theory (GVPT2) in conjunction with a hybrid force field combining the harmonic part of revDSD-PBEP86-D3/jun-cc-pVTZ with anharmonic corrections from B3LYP-D3/SNSD show very good agreement with those in the experiment, with a mean error of for all fundamental transitions overall and only for the stretching fundamental at 4.49 . The inclusion of overtones up to three-quanta transitions also allowed the prediction of spectra in the near-infrared region, which shows distinct features due to overtones at the 2.26 and 1.52 . The remarkable accuracy of the GVPT2 results opens a pathway for the reliable prediction of spectra for a broader range of cyano-astroCOMs.

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab-initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarises the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations. Program summaryProgram Title:Green/WeakCouplingCPC Library link to program files:https://doi.org/10.17632/2ysyhzww6t.1Developer's repository link:https://github.com/Green-Phys/green-mbptProgramming language:C++17, CUDA, PythonLicensing provisions: MIT LicenseExternal routines/libraries:MPI >= 3.0, BLAS, Eigen >= 3.4.0, cmake >= 3.18, cuBLAS.Nature of problem: The simulation of periodic solids and molecules using diagrammatic perturbation theorySolution method: We present an open-source implementation of the fully self-consistent finite-temperature many-body perturbation theory formalism at the GW and second-order perturbation theory level.

Accurate Vibrational and Ro-Vibrational Contributions to the Properties of Large Molecules by a New Engine Employing Curvilinear Internal Coordinates and Vibrational Perturbation Theory to Second Order.

The unbiased comparison between theory and experiment requires approaches more sophisticated than the basic harmonic-oscillator rigid-rotor model, for taking into account vibrational averaging effects and ro-vibrational couplings in molecules of increasing size. Second-order vibrational perturbation theory based on curvilinear internal coordinates (ICs) offers a remarkable compromise between accuracy and computational cost, thanks to the reduction of mode-mode couplings with respect to their counterparts based on Cartesian coordinates. Therefore, we have developed, implemented, and validated a general engine employing ICs, which allows the accurate evaluation of vibrational averages and ro-vibrational couplings for molecules containing up to about 50 atoms beyond the harmonic approximation. After validation of the new tool for relatively small molecules, the effectiveness of ICs has been demonstrated for some flexible and/or quite large molecular bricks of life.

Gravitational waves on Kerr black holes: I. Reconstruction of linearized metric perturbations

Abstract The gravitational perturbations of a rotating Kerr black hole are notoriously complicated, even at the linear level. In 1973, Teukolsky showed that their physical degrees of freedom are encoded in two gauge-invariant Weyl curvature scalars that obey a separable wave equation. Determining these scalars is sufficient for many purposes, such as the computation of energy fluxes. However, some applications -- such as second-order perturbation theory -- require the reconstruction of metric perturbations. In principle, this problem was solved long ago, but in practice, the solution has never been worked out explicitly. Here, we do so by writing down the metric perturbation (in either ingoing or outgoing radiation gauge) that corresponds to a given mode of either Weyl scalar. Our formulas make no reference to the Hertz potential (an intermediate quantity that plays no fundamental role) and involve only the radial and angular Kerr modes, but not their derivatives, which can be altogether eliminated using the Teukolsky--Starobinsky identities. We expect these analytic results to prove useful in numerical studies and for extending black hole perturbation theory beyond the linear regime.

Roles of Nonadiabatic Processes, Reaction Mechanism, and Selectivity in Cu-Catalyzed [2 + 2] Photocycloaddition of Norbornene and Acetone to Oxetane.

Oxetane has been extensively studied for its applications in medicinal chemistry and as a reactive intermediate in synthesis. Experiments report a Cu-catalyzed [2 + 2] photocycloaddition of acetone and norbornene to oxetane, which is proposed to deviate from the conventional Paternò-Büchi reaction. However, its mechanism at the atomic level is not clear. In this study, we used a combination of multistate complete active space second-order perturbation theory (MS-CASPT2) and density functional theory to systematically investigate the reaction mechanism and elucidate the factors contributing to the diastereomeric selectivity. Initially, the formation of the TpCu(Norb) complex is achieved by strong interaction between tris(pyrazolyl)borate Cu(I) (TpCu) and norbornene in the ground state (S0). Upon photoexcitation, TpCu(Norb) eventually decays to the T1 state, in which TpCu(Norb) attacks acetone to initiate subsequent reactions and produces final endo- or exo-oxetane products. All these reactions initially involve the C-C bond formation in the T1 state thereto leading to a ring-opening intermediate. This intermediate then undergoes a nonradiative transition to the S0 state, producing a five-membered ring intermediate, from which the C-O bond is formed, leading to the experimentally dominant exo-product. In contrast, the endo-oxetane formation requires a rearrangement process after the C-C bond is formed because of the large steric effects. As a consequence, the different reaction pathways generating exo- and endo-products exhibit large differences in the free-energy barriers, which results in a diastereomeric selectivity observed experimentally. Additionally, the nonradiative transition is found to play an important role in facilitating these reaction steps. The present computational study provides valuable mechanistic insights into Cu-catalyzed photocycloaddition reactions.

Spectroscopic and computational characterization of lanthanide-mediated bond activation of ethylamine

Ln (Ln = La and Ce) atom reactions with ethylamine are conducted in a pulsed laser vaporization supersonic molecular beam source. Dehydrogenation and association metal-containing species are observed with time-of-flight mass spectrometry, and the dehydrogenated Ln ethylimido species in the formula Ln(NC2H5) are characterized by single-photon mass-analyzed threshold ionization (MATI) spectroscopy and quantum chemical calculations. The theoretical calculations include density functional theory for both Ln species and a scalar relativity correction, electron correlation, and spin-orbit coupling through multiconfiguration quasi-degenerate second-order perturbation theory for the Ce species. The MATI spectrum of lanthanum ethylimido La(NCH2CH3) has a single vibronic band system from the ionization of the doublet ground state with the La 6s1 configuration, whereas that of the cerium ethylimido Ce(NCH2CH3) displays two vibronic band system from the ionization of the two lowest-energy spin-orbit coupling states with the Ce 4f16s1 configuration. Both Ln ethylimido complexes are formed by the thermodynamically and kinetically favorable concerted dehydrogenation of the amino group. Two additional isomers of Ln(NC2H5) include a four-membered metallacycle Ln(NHCH2CH2) from the dehydrogenation of the amino and methyl groups and a three-membered cycle Ln(NHCHCH3) from the dehydrogenation of the amino and methylene groups. The cyclic isomers are not observed experimentally as they are not populated under the experimental conditions.

A comparative study of measurements and numerical simulations of acoustically excited non-spherical bubbles oscillation

A detailed GPU-based parameter study is performed on the nonlinear shape deformation of acoustically excited bubbles using a second-order perturbation theory developed by Shaw (2006). The parameter scan is utilized for an extensive validation study based on a detailed measurement study conducted by Cleve et al. (2019). Out of the ten measurements, six exhibit an excellent match with the simulation results. For the discrepancies of the remaining four, the authors identified two causes. First, the parameter identification of the measurement is prone to significant error; second, the dynamics of the surface wave oscillation is out of the validity limit of the employed model.

Entropy of dynamical black holes

We propose a new formula for the entropy of a dynamical black hole—valid to leading order for perturbations off of a stationary black hole background—in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in n dimensions. In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term. In particular, in general relativity, our formula for the entropy of a dynamical black hole differs from the standard Bekenstein-Hawking formula A/4 by a term involving the integral of the expansion of the null generators of the horizon. We show that, to leading perturbative order, our dynamical entropy in general relativity is equal to 1/4 of the area of the apparent horizon. Our formula for entropy in a general theory of gravity is obtained from the requirement that a “local physical process version” of the first law of black hole thermodynamics hold for perturbations of a stationary black hole. It follows immediately that for first order perturbations sourced by external matter that satisfies the null energy condition, our entropy obeys the second law of black hole thermodynamics. For vacuum perturbations, the leading-order change in entropy occurs at second order in perturbation theory, and the second law is obeyed at leading order if and only if the modified canonical energy flux is positive (as is the case in general relativity but presumably would not hold in more general theories of gravity). Our formula for the entropy of a dynamical black hole differs from a formula proposed independently by Dong and by Wall. We obtain the general relationship between their formula and ours. We then consider the generalized second law in semiclassical gravity for first order perturbations of a stationary black hole. We show that the validity of the quantum null energy condition (QNEC) on a Killing horizon is equivalent to the generalized second law using our notion of black hole entropy but using a modified notion of von Neumann entropy for matter. On the other hand, the generalized second law for the Dong-Wall entropy is equivalent to an integrated version of QNEC, using the unmodified von Neumann entropy for the entropy of matter. Published by the American Physical Society 2024

Computational screening of metalloporphyrin catalysts for the activation of carbon dioxide

Electrocatalytic CO2 reduction (eCO2R) to value-added chemicals offers a promising route for carbon capture and utilization. Metalloporphyrin (M-POR) is a class of catalysts for eCO2R that has drawn attention due to its tuneable electronic and structural properties. This work presents a computational screening, based on density functional theory calculations, of one of the key steps in the eCO2R: the adsorption of CO2 on 110 M-PORs with varying peripheral ligands, metal centres, and oxidation states, to understand how these factors can influence CO2 activation. A set of criteria was used to shortlist M-PORs based on their ability to lengthen the C–O bond, bend the O–C–O angle, bind CO2, and donate charge from the metal of the M-POR to the carbon of CO2. 16 systems were selected for their potential to activate CO2. These systems predominantly have the electron configuration of the metal centre in the d[6] and d[7] configurations. Natural bond orbital analysis revealed the impact of electron-withdrawing groups in the system, which increases orbital splitting and, consequently, lowers the ability of the M-POR to activate CO2. Second-order perturbation theory analysis confirms that the presence of electron-donating groups in the ligand structure enhances CO2 activation. This work demonstrates the interconnected effect of peripheral ligands, metal centres, and oxidation states in M-PORs on their ability to adsorb and activate CO2, thereby establishing structure-activity relationships within M-PORs.

Infrared signature of the hydroperoxyalkyl intermediate (·QOOH) in cyclohexane oxidation: An isomer-resolved spectroscopic study.

Infrared (IR) action spectroscopy is utilized to characterize carbon-centered hydroperoxy-cyclohexyl radicals (·QOOH) transiently formed in cyclohexane oxidation. The oxidation pathway leads to three nearly degenerate ·QOOH isomers, β-, γ-, and δ-QOOH, which are generated in the laboratory by H-atom abstraction from the corresponding ring sites of the cyclohexyl hydroperoxide (CHHP) precursor. The IR spectral features of jet-cooled and stabilized ·QOOH radicals are observed from 3590 to 7010cm-1 (∼10-20kcal mol-1) at energies in the vicinity of the transition state (TS) barrier leading to OH radicals that are detected by ultraviolet laser-induced fluorescence. The experimental approach affords selective detection of β-QOOH, arising from its significantly lower TS barrier to OH products compared to γ and δ isomers, which results in rapid unimolecular decay and near unity branching to OH products. The observed IR spectrum of β-QOOH includes fundamental and overtone OH stretch transitions, overtone CH stretch transitions, and combination bands involving OH or CH stretch with lower frequency modes. The assignment of β-QOOH spectral features is guided by anharmonic frequencies and intensities computed using second-order vibrational perturbation theory. The overtone OH stretch (2νOH) of β-QOOH is shifted only a few wavenumbers from that observed for the CHHP precursor, yet they are readily distinguished by their prompt vs slow dissociation rates to OH products.

Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules.

The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.

Accurate structures and rotational constants of bicyclic monoterpenes at DFT cost by means of the bond-corrected Pisa composite scheme (BPCS).

The structural, conformational, and spectroscopic properties in the gas phase of 20 bicyclic monoterpenes and monoterpenoids have been analyzed by a new accurate, reduced-cost computational strategy. In detail, the revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion corrections and a suitable triple-zeta basis set provides accurate geometrical parameters, whence equilibrium rotational constants, which are further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental rotational constants are reached when taking into account the vibrational corrections obtained by the B3LYP functional in conjunction with a double-zeta basis set in the framework of second-order vibrational perturbation theory. In addition to their intrinsic interest, the studied terpenes further extend the panel of systems for which the proposed strategy has provided accurate results at density functional theory cost. Therefore, a very accurate yet robust and user-friendly tool is now available for systematic investigations of the role of stereo-electronic effects on the properties of large systems of current technological and/or biological interest by experimentally oriented researchers.

Ultrafast Photoinduced Dynamics in 1,3-Cyclohexadiene: A Comparison of Trajectory Surface Hopping Schemes†.

Photoinduced nonadiabatic processes play a crucial role in a wide range of disciplines, from fundamental steps in biology to modern applications in advanced materials science. A theoretical understanding of these processes is highly desirable, and trajectory surface hopping (TSH) has proven to be a well-suited framework for a wide range of systems. In this work, we present a comprehensive comparison between two TSH algorithms, the conventional Tully's fewest switches surface hopping (FSSH) scheme and the Landau-Zener surface hopping (LZSH), to study the photoinduced ring-opening of 1,3-cyclohexadiene (CHD) to 1,3,5-hexatriene at the spin-flip time-dependent density functional theory (SF-TDDFT) level of theory. Additionally, we compare our results with a literature study at the extended multistate complete active space second-order perturbation theory method (XMS-CASPT2) level of theory. Our results show that the average population and lifetimes estimated with LZSH using SF-TDDFT are closer to the literature (using multireference methods) than those estimated with FSSH using SF-TDDFT. The latter speaks in favor of applying LZSH in combination with the SF-TDDFT method to study larger and more complex systems such as molecular photoswitches where the CHD molecule acts as a backbone. In addition, we present an implementation of Tully's FSSH algorithm as an extension to the PySurf software package.

Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach.

We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.

Picking up Good Vibrations through Quartic Force Fields and Vibrational Perturbation Theory.

Quartic force fields (QFFs) define sparse potential energy surfaces (compared to semiglobal surfaces) that are the cheapest and easiest means of computing anharmonic vibrational frequencies, especially when utilized with second-order vibrational perturbation theory (VPT2). However, flat and shallow potential surfaces are exceedingly difficult for QFFs to treat through a combination of numerical noise in the often numerically computed derivatives and in competing energy factors in the composite energies often utilized to provide high-level spectroscopic predictions. While some of these issues can be alleviated with analytic derivatives, hybrid QFFs, and intelligent choices in coordinate systems, the best practice is for predicting good molecular vibrations via QFFs is to understand what they cannot do, and this manuscript documents such cases where QFFs may fail.

Electric dipole polarizability of low-lying excited states in atomic nuclei

New equations for the electric dipole polarizability α E1 of low-lying excited states in atomic nuclei—and the related (−2) moment of the total photo-absorption cross section, σ −2—are inferred in terms of electric dipole and quadrupole matrix elements. These equations are valid for arbitrary angular momenta of the initial/ground and final/excited states and have been exploited in fully converged 1ℏ ω shell-model (SM) calculations of selected p- and sd-shell nuclei that consider configuration mixing; advancing previous knowledge from 17O to 36Ar, where thousands of electric dipole matrix elements are computed from isovector excitations which include the giant dipole resonance (GDR) region. Our results are in reasonable agreement with previous SM calculations and follow—except for 6,7Li and 17,18O—Migdal’s global trend provided by the combination of the hydrodynamic model and second-order non-degenerate perturbation theory. Discrepancies in 6,7Li and 17O arise as a result of the presence of α-cluster configurations in odd-mass nuclei, whereas the disagreement in 18O comes from the mixing of intruder states, which is lacking in the SM interactions. More advanced ab initio calculations of the dipole polarizability for low-lying excited states covering all the isovector states within the GDR region are missing and could be very valuable to benchmark the results presented here and shed further light on how atomic nuclei polarize away from the ground state

Fractonic quantum quench in dipole-constrained bosons

We investigate the quench dynamics in the dipolar Bose-Hubbard model (DBHM) in one dimension. The boson hopping is constrained by dipole conservation and shows fractonic dynamics. The ground states at large Hubbard interaction U are Mott insulators at integer filling and a period-2 charge density wave (CDW) at half-integer filling. We focus on Mott-to-Mott and CDW-to-CDW quenches and find that dipole correlation spreading shows the light-cone behavior with the Lieb-Robinson (LR) velocity proportional to the dipole kinetic energy J and the square of the density in the case of Mott quench at integer filling. An effective model for postquench dynamics is constructed under the dilute-dipole approximation and fits the numerical results well. For the CDW quench, we observe a much reduced LR velocity of order J2/U and additional periodic features in the time direction. The emergence of a CDW ground state and the reduced LR velocity at half-integer filling can both be understood by careful application of the second-order perturbation theory. The oscillatory behavior arises from quantum scars in the quadrupole sector of the spectrum and is captured by a PXP-like model that we derive by projecting the DBHM to the quadrupolar sector of the Hilbert space. Published by the American Physical Society 2024

Computational study on the electronic states of tungsten nitride molecule

The state-averaged complete active space self-consistent field (SA-CASSCF) method and rotated multi-state complete active space second-order perturbation theory (RMS-CASPT2) are applied to investigate the low-lying Λ–S and Ω electronic states of tungsten nitride, WN. The potential energy curves of the low-lying states are computed, and the fitted spectroscopic constants are in good agreement with the available experimental results. The A4Π-X4Σ- transition is focused to compare with the previously observed emission spectra of WN in the region of 500–580 nm. With the inclusion of the spin–orbit coupling, the ground Λ–S state X4Σ- and the excited state A4Π split into 4Σ− 1/2, 3/2 and 4Π−1/2, 1/2, 3/2, 5/2, respectively; and according to the present computed results, in conjunction with the results from previous studies, a complete set of transition data for the WN molecule is obtained. Our computed results indicate that the observed spectra should be assigned to the fine structure of A4Π-X4Σ- transition in WN. Furthermore, spectra information, including transition energy and transition dipole moment, arising from the transitions from the other excited states to ground states is also predicted. It is expected that the present work would promote the further experimental studies on absorption or emission spectra of WN.

General framework for quantifying dissipation pathways in open quantum systems. I. Theoretical formulation.

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.

A Spectroscopic and Computational Evaluation of Uranyl Oxo Engagement with Transition Metal Cations.

We report the synthesis and characterization of five novel Cd2+/UO22+ heterometallic complexes that feature Cd-oxo distances ranging from 78 to 171% of the sum of the van der Waals radii for these atoms. This work marks an extension of our previously reported Pb2+/UO22+ and Ag+/UO22+ complexes, yet with much more pronounced structural and spectroscopic effects resulting from Cd-oxo interactions. We observe a major shift in the U═O symmetric stretch and significant uranyl bond length asymmetry. The ρbcp values calculated using Quantum Theory of Atoms in Molecules (QTAIM) support the asymmetry displayed in the structural data and indicate a decrease in covalent character in U═O bonds with close Cd-oxo contacts, more so than in related compounds containing Pb2+ and Ag+. Second-order perturbation theory (SOPT) analysis reveals that O spx → Cd s is the most significant orbital overlap and U═O bonding and antibonding orbitals also contribute to the interaction (U═O σ/π → Cd d and Cd s → U═O σ/π*). The overall stabilization energies for these interactions were lower than those in previously reported Pb2+ cations, yet larger than related Ag+ compounds. Analysis of the equatorial coordination sphere of the Cd2+/UO22+ compounds (along with Pb2+/UO22+ complexes) reveals that 7-coordinate uranium favors closer, stronger Mn+-oxo contacts. These results indicate that U═O bond strength tuning is possible with judicious choice of metal cations for oxo interactions and equatorial ligand coordination.