Second-order Perturbation Theory Research Articles

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.

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

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.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Infrared spectroscopy of the syn-methyl-substituted Criegee intermediate: A combined experimental and theoretical study.

An IR-vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR-VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081cm-1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Two-photon absorption in quantum dots with Hellmann potential

Abstract We study the nonlinear optical absorption properties of a spherical quantum dot (SQD) with Hellmann potential, focusing on the two-photon absorption (TPA) process, using GaAs/AlGaAs material as an example. The radial Schrödinger equation is solved using the Nikiforov-Uvarov method, while the two-photon absorption coefficient is determined through second-order perturbation theory concerning the electron-photon interaction. Our study shows that the intraband transition has a smaller energy transition than the interband transition, leading to TPA spectra for the intraband transition that is restricted within a smaller energy range and exhibits a higher peak value than those for the interband transition. The peak corresponding to the orbital quantum number of electrons in SQD ℓ = 2 consistently appears to the left of the peak corresponding to ℓ = 1 in both intraband and interband transition cases. Additionally, the dependence of the absorption peak position on the order of transition, n, differs between intra- and inter-band transitions. We also observe blue shift behavior in the TPA spectra as all three parameters, r 0, V 0e , and η, increase. Our investigation has the potential to enable the design of novel photonic devices, ultra-fast optical switches, and highly efficient solar cells through the optimization of quantum dot material properties.

Quasi-degenerate extension of local N-electron valence state perturbation theory with pair-natural orbital method based on localized virtual molecular orbitals.

Chemical phenomena involving near-degenerate electronic states, such as conical intersections or avoided crossing, can be properly described using quasi-degenerate perturbation theory. This study proposed a highly scalable quasi-degenerate second-order N-electron valence state perturbation theory (QD-NEVPT2) using the local pair-natural orbital (PNO) method. Our recent study showed an efficient implementation of the PNO-based state-specific NEVPT2 method using orthonormal localized virtual molecular orbitals (LVMOs) as an intermediate local basis. This study derived the state-coupling (or off-diagonal) terms to implement QD-NEVPT2 in an alternative manner to enhance efficiency based on the internally contracted basis and PNO overlap matrices between different references. To facilitate further acceleration, a local resolution-of-the-identity (RI) three-index integral generation algorithm was developed using LMOs and LVMOs. Although the NEVPT2 theory is considered to be less susceptible to the intruder-state problem (ISP), this study revealed that it can easily suffer from ISP when calculating high-lying excited states. We ameliorated this instability using the imaginary level shift technique. The PNO-QD-NEVPT2 calculations were performed on small organic molecules for the 30 lowest-lying states, as well as photoisomerization involving the conical intersection of 1,1-dimethyldibenzo[b,f] silepin with a cis-stilbene skeleton. These calculations revealed that the PNO-QD-NEVPT2 method yielded negligible errors compared to the canonical QD-NEVPT2 results. Furthermore, we tested its applicability to a large photoisomerization system using the green fluorescent protein model and the ten-state calculation of the large transition metal complex, showcasing that off-diagonal elements can be evaluated at a relatively low cost.

Ab Initio Calculation of UV-vis Absorption of Parent Mg, Fe, Co, Ni, Cu, and Zn Metalloporphyrins.

Relativistic restricted active space (RAS) second-order multireference perturbation theory (MRPT2) methods, incorporating spin-orbit (SO) coupling perturbatively via state interaction (SO-MRPT2/RASSCF), were used to reproduce the absorption spectra of parent metalloporphyrins containing the Mg2+, Zn2+, Co2+, Ni2+, Cu2+, or FeCl2+ ions in the 12,500-40,000 cm-1 region. Particular attention was paid to the interaction between the porphyrin ring and the metal 3d electrons in states of different multiplicities (we used metal 3d and double d-shell or 3d' orbitals). For this class of compounds, the N-electron valence state perturbation theory (NEVPT2) method is superior to the complete active space perturbation theory (CASPT2) and successfully reproduces the energies of all four characteristic transitions (Q, B, N, and L) of closed-shell metalloporphyrins. Inclusion of SO coupling was found to have very little effect on excitation energies and oscillator strengths. For FeCl2+ porphyrin, we treated ligand-to-metal charge-transfer (LMCT; π,d), metal ligand field (d,d), and metal-to-ligand charge-transfer (MLCT; d,π*) transitions within the same framework. The broad and intense spectral features associated with its B (Soret) band are attributed to multiconfigurational LMCT (d,π*) bands involving strong metal-ligand orbital mixing.

Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group.

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

ℏ 4 quantum corrections to semiclassical transmission probabilities

The combination of vibrational perturbation theory with the replacement of the harmonic oscillator quantization condition along the reaction coordinate with an imaginary action to be used in the uniform semiclassical approximation for the transmission probability has been shown in recent years to be a practical method for obtaining thermal reaction rates. To date, this theory has been developed systematically only up to second order in perturbation theory. Although it gives the correct leading order term in an ℏ2 expansion, its accuracy at lower temperatures, where tunneling becomes important, is not clear. In this paper, we develop the theory to fourth order in the action. This demands developing the quantum perturbation theory up to sixth order. Remarkably, we find that the fourth order theory gives the correct ℏ4 term in the expansion of the exact thermal rate. The relative magnitude of the fourth order correction as compared to the second order term objectively indicates the accuracy of the second order theory. We also extend the previous modified second order theory to the fourth order case, creating an ℏ2 modified potential for this purpose. The resulting theory is tested on the standard examples—symmetric and asymmetric Eckart potentials and a Gaussian potential. The modified fourth order theory is remarkably accurate for the asymmetric Eckart potential.

Probing Ion-Receptor Interactions in Halide Complexes of Octamethyl Calix[4]Pyrrole.

Ion receptors are molecular hosts that bind ionic guests, often with great selectivity. The interplay of solvation and ion binding in anion host-guest complexes in solution governs the binding efficiency and selectivity of such ion receptors. To gain molecular-level insight into the intrinsic binding properties of octamethyl calix[4]pyrrole (omC4P) host molecules with halide guest ions, we performed cryogenic ion vibrational spectroscopy (CIVS) of omC4P in complexes with fluoride, chloride, and bromide ions. We interpret the spectra using density functional theory, describing the infrared spectra of these complexes with both harmonic and anharmonic second-order vibrational perturbation theory (VPT2) calculations. The NH stretching modes of the pyrrole moieties serve as sensitive probes of the ion binding properties, as their frequencies encode the ion-receptor interactions. While scaled harmonic spectra reproduce the experimental NH stretching modes of the chloride and bromide complexes in broad strokes, the high proton affinity of fluoride introduces strong anharmonic effects. As a result, the spectrum of F-·omC4P is not even qualitatively captured by harmonic calculations, but it is recovered very well by VPT2 calculations. In addition, the VPT2 calculations recover the intricate coupling of the NH stretching modes with overtones and combination bands of CH stretching and NH bending modes and with low-frequency vibrations of the omC4P macrocycle, which are apparent for all of the halide ion complexes investigated here. A comparison of the CIVS spectra with infrared spectra of solutions of the same ion-receptor complexes in d3-acetonitrile and d6-acetone shows how ion solvation changes the ion-receptor interactions for the different halide ions.

Quantum-Chemistry Study of the Photophysical Properties of 4-Thiouracil and Comparisons with 2-Thiouracil.

DNA in living beings is constantly damaged by exogenous and endogenous agents. However, in some cases, DNA photodamage can have interesting applications, as it happens in photodynamic therapy. In this work, the current knowledge on the photophysics of 4-thiouracil has been extended by further quantum-chemistry studies to improve the agreement between theory and experiments, to better understand the differences with 2-thiouracil, and, last but not least, to verify its usefulness as a photosensitizer for photodynamic therapy. This study has been carried out by determining the most favorable deactivation paths of UV-vis photoexcited 4-thiouracil by means of the photochemical reaction path approach and an efficient combination of the complete-active-space second-order perturbation theory//complete-active-space self-consistent field (CASPT2//CASSCF), (CASPT2//CASPT2), time-dependent density functional theory (TDDFT), and spin-flip TDDFT (SF-TDDFT) methodologies. By comparing the data computed herein for both 4-thiouracil and 2-thiouracil, a rationale is provided on the relatively higher yields of intersystem crossing, triplet lifetime and singlet oxygen production of 4-thiouracil, and the relatively higher yield of phosphorescence of 2-thiouracil.

Can Iron-Porphyrins Behave as Single-Molecule Magnets?

The study of magnetic properties, especially the magnetic anisotropy of iron-porphyrin complexes employing multiconfigurational methods, is quite challenging due to many strongly correlated electrons in nearly degenerate orbitals. However, a prerequisite for observing the magnetic anisotropy and slow magnetization relaxation, the zero-field splitting parameter, D, was experimentally observed decades ago for halide-based axially ligated penta-coordinate Fe(III)-porphyrins. In these complexes, the signs of D were reported mostly as positive; in a few cases, inconclusive signs of the D parameter were also mentioned. However, no ab initio calculations have been reported to shed light on this. Deciphering the electronic structure of these penta-coordinated complexes employing the complete active space self-consistent field method and N-electron valence second-order perturbation theory, we confirm the positive D values. However, a negative D value is highly desired to observe the single-molecule magnet properties without an external magnetic field, which we observed in the Fe(II)-porphyrin complexes with axial imidazole ligands instead of halide ligands. The detailed analysis of the multireference wave functions unravels the role of axial ligands in determining the sign and magnitude of the D parameters.

Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density.

Lagrangians of the state-averaged multiconfigurational self-consistent field (SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density are defined. In addition, variational equations were derived to calculate the excitation energies of the target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions, and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines, including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role in predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene).

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions.

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

Ab Initio Conformational Analysis of 3,7-Diacetyl-3,7-Diazabicyclo[3.3.1]Nonanes

Introduction: The importance of the conformational behavior comprehension for proper prediction of properties for a certain compound or for a class of compounds is indisputable. For 3,7-diacylbispidines (3,7-diacyl-3,7-diazabicyclo[3.3.1]nonanes), only “double chair” (CC) conformers were prior found experimentally in the condensed phase, which differ only in the acyl groups relative orientation, “parallel,” pa or “antiparallel,” ap. However, 2 other conformer families, “boat-chair,” BC and “double twist,” TT, are known for other bicyclo[3.3.1]nonane derivatives. Features of these conformers would be useful for the accurate prediction of properties and activities of the compounds. Methods: Second-order perturbation theory ab initio techniques (MP2) in the triple-zeta correlation-consistent orbital basis set cc-pVTZ was employed to optimize the electronic energy for structures, to characterize the optimized structures as potential energy surface minima by energy hessian eigenvalue calculations and to calculate zero-point energy corrections for the minima using the “rigid rotor-harmonic oscillator” approximation to model the molecular ensemble thermodynamics. Additionally, the computational chemical thermodynamics benefits much from the concept of the molecular strain and its energy assessed successfully through the bond separation energy formalism. We combine both approaches in our investigation to find and consistently characterize the conformers previously unknown for the compounds under the studies. Results: Six possible conformers were found for the investigated 3,7-diacetyl-3,7-diazabicyclo[3.3.1]nonanes 1-4, formed by combining the skeletal conformation changes with the internal rotation of acyl substituents. The conformational behavior is quite similar for all investigated molecules. In all cases, the CC conformation is optimal for the bicyclic skeleton and ap orientation prevails over pa for 2 acetyl groups. This prevalence is 4-5 kcal mol−1 in CC and less than 1 kcal mol−1 in other skeletal forms, making rotation of 2 acyl groups in BC and TT almost independent. Concerning the skeletal conformations, the common energy sequence CC < BC < TT is found. While the relative BC energy is 6-7 kcal mol−1 over the optimal CC structure, TT forms are all strained by more than 12 kcal mol−1. Conclusions: For the first time, both BC and TT conformers of 3,7-diacetylbispidines were characterized by their strain and conformation energies together with known less strained CC forms. On the basis of our calculations, the relative energies of BC conformers are expected to be close to those of the CC acetyl amide bond rotamers found previously in experiment, therefore, their exclusion from the conformational behavior would look unjustified. On the contrary, TT conformers are found to be much more strained enough to be neglected in the conformational ensemble modeling.

Exploration of the Two-Electron Excitation Space with Data-Driven Coupled Cluster.

Computational cost limits the applicability of post-Hartree-Fock methods such as coupled-cluster on larger molecular systems. The data-driven coupled-cluster (DDCC) method applies machine learning to predict the coupled-cluster two-electron amplitudes (t2) using data from second-order perturbation theory (MP2). One major limitation of the DDCC models is the size of training sets that increases exponentially with the system size. Effective sampling of the amplitude space can resolve this issue. Five different amplitude selection techniques that reduce the amount of data used for training were evaluated, an approach that also prevents model overfitting and increases the portability of data-driven coupled-cluster singles and doubles to more complex molecules or larger basis sets. In combination with a localized orbital formalism to predict the CCSD t2 amplitudes, we have achieved a 10-fold error reduction for energy calculations.