Second-order Perturbation Theory Research Articles

Water Solvated Zn(II)-Guanine Complex: Structural Aspects and Luminescence Properties.

Understanding the role of metal ions in living organisms and their interactions with biological compounds is fundamental for our health and for developing technological devices for bioinorganic applications. In this work, structural aspects and photophysical mechanisms involved in the luminescence of the Zn(II)-guanine complex in water were studied by using computational quantum chemical methods, providing molecular-level explanations for reported experimental findings. Structural aspects were investigated with def2-SVP basis sets, Density Functional Theory, Resolution of Identity Algebraic Diagrammatic Construction in Second-Order (RI-ADC(2)), Polarizable Continuum Model (PCM), and Conductor-like Screening Model (COSMO) methods. Spectroscopic properties and photophysical deactivation mechanisms were explored with the atomic natural orbital basis sets including relativistic and semicore correlation (ANO-RCC-VDZP) basis sets, Multistate Complete-Active-Space Second-Order Perturbation Theory (MS-CASPT2), and Polarizable Continuum Model (PCM) methods. Our results indicate that Zn(II) ions bind preferentially to the N7 position, and three water molecules in its coordination sphere are sufficient for describing the photophysical properties. The complexation with Zn(II) ions and solvation effects favor fluorescence because the minimum energy region of the S1 (La) (1ππ*) ((La)min) potential energy hypersurface is stabilized, the (La/GS) crossing region is destabilized, and a high energetic barrier along the pathway from the (La)min and (La/GS) regions hampers fast nonradiative return of the electronic population to the ground state, as observed for isolated 9H-guanine.

Post-Kohn-Sham Random-Phase Approximation and Correction Terms in the Expectation-Value Coupled-Cluster Formulation.

Using expectation-value coupled-cluster theory and many-body perturbation theory (MBPT), we formulate a series of corrections to the post-Kohn-Sham (post-KS) random-phase approximation (RPA) energy. The beyond-RPA terms are of two types: those accounting for the non-Hartree-Fock reference and those introducing the coupled-cluster doubles non-ring contractions. The contributions of the former type, introduced via the semicanonical orbital basis, drastically reduce the binding strength in noncovalent systems. The good accuracy is recovered by the attractive third-order doubles correction referred to as Ec2g. The existing RPA approaches based on KS orbitals neglect most of the proposed corrections but can perform well thanks to error cancellation. The proposed method accounts for every contribution in the state-of-the-art renormalized second-order perturbation theory (rPT2) approach but adds additional terms which initially contribute in the third order of MBPT. The cost of energy evaluation scales as noniterative in the implementation with low-rank tensor decomposition. The numerical tests of the proposed approach demonstrate accurate results for noncovalent dimers of polar molecules and for the challenging many-body noncovalent cluster of CH4···(H2O)20.

Fundamental vibrational frequencies of pnictogen (Pn) containing linear triatomic anions: OCPn - and SCPn - where Pn = N, P, As and Sb

The fundamental vibrational frequencies of the isolated OCAs − and SCAs − ions, as well as their heavier antimony analogues, are reported for the first time. A thorough analysis of basis set convergence of the bond lengths and harmonic vibrational frequencies, as well as the examination of anharmonic corrections, is conducted using the MP2 and CCSD(T) ab initio methods with robust basis sets for the OC P n − and SC P n − anions moving down the pnictogen series from Pn = N to Sb. Second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) theory are used to compute the fundamental vibrational frequencies of each triatomic anion approaching the MP2 and CCSD(T) complete basis set (CBS) limits. While fundamental vibrational frequencies have been reported for OCN − and SCN − in the gas phase, only experimental vibrational frequencies of the salts for the heavier pnictogen analogues (P and As) have been reported. Experimental Raman vibrational frequencies for OCAs − and SCAs − salts were found to be coincidentally in good agreement with the CCSD(T) VCI frequencies near the CBS limit, differing by at most 13 cm − 1 from the former and 9 cm − 1 from the latter. These modest differences are likely due to the presence of counter-ions and other environmental effects in the solid state, and the overall agreement between the salts and gas-phase frequencies is quite similar to that observed for the OCP − and SCP − ions.

Revealing the effect of phase and time coupling on NMR relaxation rate by random walks in phase space.

Phase-time coupling is a natural process in the phase random walks of a spin system; however, its effect on the nuclear magnetic resonance (NMR) relaxation is a challenge to the established theories such as the second-order quantum perturbation theory. This paper extends the recently developed phase diffusion method to treat the phase-time coupling effect, based on uncoupled phase diffusions, and coupled random walks. The instantaneous projection of the rotating random field is employed to get the accumulated phase of the NMR observable. In the static frame and the rotating frame, the phase diffusion coefficients are derived. The obtained theoretical results show that the phase-time coupling has a significant impact on the NMR relaxation rate: The angular frequency ω in the spectral density is modified to an apparent angular frequency ηω, where η is the phase-time coupling constant. The strongest coupling has η equaling 2, while η equaling 1 corresponds to the traditional results. As an example, the modified relaxation time expressions based on both monoexponential and nonmonoexponential functions can successfully fit the previously reported ^{13}CT_{1} NMR experimental data of polyisobutylene (PIB) in the blend of PIB and head-to-head poly(propylene). In contrast, the traditional relaxation rate expression based on the monoexponential time correlation function cannot fit such experimental data. With the phase-time coupling, the obtained characteristic time of the segmental motion is faster than that from conventional results.

Intruder-free cumulant-truncated driven similarity renormalization group second-order multireference perturbation theory.

Accurate multireference electronic structure calculations are important for constructing potential energy surfaces. Still, even in the case of low-scaling methods, their routine use is limited by the steep growth of the computational and storage costs as the active space grows. This is primarily due to the occurrence of three- and higher-body density matrices or, equivalently, their cumulants. This work examines the effect of various cumulant truncation schemes on the accuracy of the driven similarity renormalization group second-order multireference perturbation theory. We test four different levels of three-body reduced density cumulant truncations that set different classes of cumulant elements to zero. Our test cases include the singlet-triplet gap of CH2, the potential energy curves of the XΣg+1 and AΣu+3 states of N2, and the singlet-triplet splittings of oligoacenes. Our results show that both relative and absolute errors introduced by these cumulant truncations can be as small as 0.5kcal mol-1 or less. At the same time, the amount of memory required is reduced from O(NA6) to O(NA5), where NA is the number of active orbitals. No additional regularization is needed to prevent the intruder state problem in the cumulant-truncated second-order driven similarity renormalization group multireference perturbation theory methods.

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory.

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.

Approximating large-basis coupled-cluster theory vibrational frequencies using focal-point approximations.

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller-Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm-1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.

Dynamic Correlation on the Adaptive Sampling Configuration Interaction (ASCI) Reference Function: ASCI-DSRG-MRPT2.

A balanced description of static and dynamic electron correlations is at the heart of quantum chemical methods. To obtain accurate results in strongly correlated systems using wave-function-based methods, a large active space is necessary to ensure correct descriptions of static correlations. Correcting the results for dynamic correlations is also necessary. In this work, we present implementations of second-order perturbation theory for dynamic correlations based on the adaptive sampling configuration interaction self-consistent field (ASCI-SCF) method. In particular, we implemented spin-free driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2). The extrapolation of the ASCI + PT2 energy based on the relaxed Hamiltonian in DSRG-MRPT2 gives a reasonable approximation of DSRG-MRPT2 based on CASSCF. We demonstrate the application of the ASCI-DSRG-MRPT2 method in evaluations of the spin-state energy gaps in iron porphyrins, polyacenes, and periacenes along with the reaction energies of methane oxidation by FeO+ and electrocyclic ring formation in cethrene.

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding.

The optical spectra of neutral oxygen vacancies (F0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.

Interpolating Wilson loops and enriched RG flows

We study new 1/24 BPS circular Wilson loops in ABJ(M) theory, which are defined in terms of several parameters that continuously interpolate between previously known 1/6 BPS loops (both bosonic and fermionic) and 1/2 BPS fermionic loops. We compute the expectation value of these operators up to second order in perturbation theory using a one-dimensional effective field theory approach. Within dimensional regularization, we find non-trivial β-functions for the parameters, which are marginally relevant deformations triggering RG flows from a UV fixed point represented by the 1/6 BPS bosonic loop to an IR fixed point represented by a 1/2 BPS fermionic loop. Generically, along all flows at least one supercharge of the theory is preserved, so that we refer to them as enriched RG flows. In particular, fixed points are connected through 1/6 BPS fermionic operators. This holds at framing zero, which is a consequence of the regularization scheme employed. We also establish the validity of the g-theorem, relating the expectation values of the Wilson loops corresponding to the UV and IR fixed points of the flow, and discuss the one-dimensional defect SCFT living on the Wilson loop contour.

The performance of approximate equation of motion coupled cluster for valence and core states of heavy element systems

The equation of motion coupled cluster singles and doubles model (EOM-CCSD) is an accurate, black-box correlated electronic structure approach to investigate electronically excited states and electron attachment or detachment processes. It has also served as a basis for developing less computationally expensive approximate models such as partitioned EOM-CCSD (P-EOM-CCSD), the second-order many-body perturbation theory EOM (EOM-MBPT(2)) and their combination (P-EOM-MBPT(2)) [S. Gwaltney et al., Chem. Phys. Lett. 248, 189–198 (1996)]. In this work we outline an implementation of these approximations for four-component based Hamiltonians and investigate their accuracy relative to EOM-CCSD for valence excitations, valence and core ionisations and electron attachment, and this for a number of systems of atmospheric or astrophysical interest containing elements across the periodic table. We have found that across the different systems and electronic states of different nature considered, partition EOM-CCSD yields results with the largest deviations from the reference, whereas second-order based approaches tend show a generally better agreement with EOM-CCSD. We trace this behaviour to the imbalance brought about by the removal of excited state relaxation in the partition approaches, with respect to degree of electron correlation recovered.

Flying characterization of colliding partners by hyperfine splitting frequency of neutral paramagnetic atoms.

The pseudopotentials and dispersion potentials are applied to a theoretical study of the hyperfine splitting frequencies of the ground-state paramagnetic hydrogen (H) and alkali-metal (Li, Na, K, Rb, and Cs) atoms in noble gases (He, Ne, Ar, Kr, and Xe). Using classical turning points for statistical averages, we find that numerical calculations based on second-order perturbation theory fit the measured frequency shifts well over a wide temperature range. The characteristic energy, pseudopotential height, and electric-dipole polarizability allow us to consistently determine the van der Waals radii and electron scattering lengths of noble-gas atoms. This study shows that the hyperfine splitting frequency of alkali-metal atoms is a good measure for investigating colliding partners.

Theoretical study of low-lying electronic states of rhenium monoxide (ReO)

In this paper we report a theoretical investigation of the low-lying electronic states of the ReO molecule by using the recently developed static–dynamic–static second-order perturbation theory. The results confirm the previous experimental finding that the ground state of ReO is 2Δ or 2Δ5/2 after considering spin–orbit coupling. With the aid of the theoretical spectroscopic constants and transition dipole moments, fourteen band systems in emission spectra of ReO reported nearly 40 years ago have finally been assigned to the calculated Ω states. Our results should be of value for further experimental and theoretical studies of the spectra of ReO.

Synchronizing the consistency relation

We study the N-point function of the density contrast to quadratic order in the squeezed limit during the matter-dominated (MD) and radiation-dominated (RD) eras in synchronous gauge. Since synchronous gauge follows the free-fall frame of observers, the equivalence principle dictates that in the gradient approximation for the long-wavelength mode there is only a single, manifestly time-independent consistency relation for the N-point function. This simple form is dictated by the initial mapping between synchronous and local coordinates, unlike Newtonian gauge and its correspondingly separate dilation and Newtonian consistency relations. Dynamical effects only appear at quadratic order in the squeezed limit and are again characterized by a change in the local background, also known as the separate universe approach. We show that for the 3-point function the compatibility between these squeezed-limit relations and second-order perturbation theory requires both the initial and dynamical contributions to match, as they do in single-field inflation. This clarifies the role of evolution or late-time projection effects in establishing the consistency relation for observable bispectra, which is especially important for radiation acoustic oscillations and for establishing consistency below the matter-radiation equality scale in the MD era. Defining an appropriate angle and time average of these oscillations is also important for making separate universe predictions of spatially varying local observables during the RD era, which can be useful for a wider range of cosmological predictions beyond N-point functions.

Comprehensive Perturbation Approach to Nonlinear Viscous Gravity–Capillary Surface Waves at Arbitrary Wavelengths in Finite Depth

This study presents a comprehensive analysis of the second-order perturbation theory applied to the Navier–Stokes equations governing free surface flows. We focus on gravity–capillary surface waves in incompressible viscous fluids of finite depth over a flat bottom. The amplitude of these waves is regarded as the perturbation parameter. A systematic derivation of a nonlinear-surface-wave equation is presented that fully takes into account dispersion, while nonlinearity is included in the leading order. However, the presence of infinitely many over-damped modes has been neglected and only the two least-damped modes are considered. The new surface-wave equation is formulated in wave-number space rather than real space and nonlinear terms contain convolutions making the equation an integro-differential equation. Some preliminary numerical results are compared with computational-modelling data obtained via open source CFD software OpenFOAM.

Photophysics of tz Adenine and tz Guanine fluorescent nucleobases embedded into DNA and RNA.

UV-VIS photoinduced events of tz A and tz G embedded into DNA and RNA are described by combining the Extended Multi-State Second-Order Perturbation Theory (XMS-CASPT2) and electrostatic embedding molecular mechanics methods (QM/MM). Our results point out that the S1 1 (ππ* La ) state is the bright state in both environments. After the photoexcitation to the S1 1 (ππ* La ) state, the electronic population evolves barrierless towards its minimum, from where the excess of energy can be dissipated by fluorescence. As the minimum energy crossing point structure between the ground and first bright states lies in a high-energy region, the direct internal conversion to the ground state is an unviable mechanism. Other spectroscopic properties (for instance, absorption and Stokes shifts) and comparisons with photochemical properties of canonical nucleobases are also provided.

First-principles molecular dynamics simulation study on Ti/Mn ions in aqueous sulfuric acid for use in redox flow battery

The effect of the Ti4+ ion on the structural and chemical features of the Mn3+ ion in aqueous sulfuric acid was investigated using first-principles molecular dynamics (FPMD) simulation and second-order perturbation theory (CASPT2) with a complete active space self-consistent field (CASSCF) reference function. The focus was on the role of the Ti ion in the MnO2 formation reaction from the Mn3+ ion. The simulations showed that Mn3+ forms two types of complexes, [Mn(H2O)4(SO4)2]1− and [Mn(H2O)6]3+ in aqueous sulfuric acid with Ti ions where the population of the former was found to be higher than that of the latter. We found that when the HSO4− ion was coordinated to a Ti4+ ion, it released one proton, which increases proton concentration in the solution. Detailed quantum chemical calculations on the isolated Mn complexes show that if the Mn complexes interact with a hydronium ion, the stability of Mn3+ ion is increased to a large extent. Such a result implies that the increased local proton concentration due to Ti4+ ions hinders formation of MnO2 particle.

Semiclassical Multistate Dynamics for Six Coupled 5A' States of O + O2.

Dynamics simulations of high-energy O2-O collisions play an important role in simulating thermal energy content and heat flux in flows around hypersonic vehicles. To carry out such dynamics simulations efficiently requires accurate global potential energy surfaces and (in most algorithms) state couplings for many energetically accessible electronic states. The ability to treat collisions involving many coupled electronic states has been a challenge for decades. Very recently, a new diabatization method, the parametrically managed diabatization by deep neural network (PM-DDNN), has been developed. The PM-DDNN method uses a deep neural network architecture with an activation function parametrically dependent on input data to discover and fit the diabatic potential energy matrix (DPEM) as a function of geometry, and the adiabatic potential energy surfaces are obtained by diagonalization of a small matrix with analytic matrix elements. Here, we applied the PM-DDNN method to the six lowest-energy potential energy surfaces in the 5A' manifold of O3 to perform simultaneous diabatization and fitting; the data are obtained by extended multistate complete-active-space second-order perturbation theory. We then used the adiabatic surfaces for dynamics calculations with three methods: coherent switching with decay of mixing (CSDM), curvature-driven CSDM (κCSDM), and electronically curvature-driven CSDM (eκCSDM). The κCSDM calculations require only adiabatic potential energies and gradients. The three dynamical methods are in good agreement. We then calculated electronically nonadiabatic, electronically inelastic, and dissociative cross sections for seven initial collision energies, five initial vibrational levels, and four initial rotational levels. Trends in the electronically inelastic cross sections as functions of the initial collision energy and vibrational level were rationalized in terms of the coordinate ranges where the gaps between the second and third potential energy surfaces are small.

Anti Microbial Activity, Vibrational, Electronic and Topology Analysis of 3, 4, 5-Trimethoxybenzaldehyde

The density functional theory (DFT) approach has become one of the most gainful means to scrutinize the molecular structure and vibrational spectra are finding well-known use in the applications related to biological systems. The experimental and theoretical on the molecular structure, electronic, and characteristics of 3, 4, 5-Trimethoxybenzaldehyde (TMB) are reported. The structure of the molecule was optimized and structural characteristics were determined by DFT using the wb97xd method with 6-311 G++ (d, p) basis sets. The vibrational assignments were made on the basis of potential energy distribution. A good consistency between the observed and calculated spectra was achieved. The intramolecular charge transfer and second-order perturbation theory of Fock Matrix in Natural bond orbital analysis by means NBO analysis. It shows the electronic stability of the compound arising from hyper conjugative interactions and charge delocalization of that molecule. Besides, the HOMO-LUMO, MEP, and Fukui were performed. In this review, the present benzaldehyde derivatives for skirmishing against bacteria strain Escherichia coli and fungi strain Candida Sp. Spectral and quantum chemical calculations are also discussed.

Hyperfine and P, T odd properties in BiO: comparison between coupled-cluster method and multi-reference perturbation method based on a Dirac Hamiltonian

Polar diatomic molecules are attractive in the search for the electron electric dipole moment (eEDM) and the scalar-pseudoscalar (S-PS) interaction, both of which violate time-reversal and parity symmetries. In this study, we examined the electronic ground state of BiO and evaluated the effective electric field (E eff) of eEDM and the W s coefficients of the S-PS interaction. BiO forms a complex chemical bond due to the open-shell configurations of Bi (6p) and O (2p). Consequently, we performed four-component relativistic calculations using complete-active-space second-order perturbation theory (CASPT2), as well as coupled-cluster singles and doubles (CCSD) and CCSD perturbative triples (CCSD(T)) methods. Our analysis revealed that BiO exhibited a multiconfigurational character, as the Hartree-Fock configuration accounted for only 68% of the reference wave function for CASPT2. Nevertheless, for the hyperfine coupling constant (A//), CCSD and CCSD(T) reproduced the experimental value better than CASPT2, indicating that CC methods can capture important excited configurations, rendering multireference treatment unnecessary. The deficiency of CASPT2 in reproducing A// could be attributed to the inadequate treatment of orbital relaxation effects. Our proposed values of E eff and W s for BiO (17 GV/cm and −36 kHz, respectively), derived at the CCSD level, were moderately large for the parity, time-odd experiment.