Hyperpolarizability of H2O

Toward Reliable Dipole Moments without Single Excitations: The Role of Orbital Rotations and Dynamical Correlation

The dipole moment is a crucial molecular property linked to a molecular system's bond polarity and overall electronic structure. To that end, the electronic dipole moment, which results from the electron density of a system, is often used to assess the accuracy and reliability of new electronic structure methods. This work analyses electronic dipole moments computed with the pair coupled cluster doubles (pCCD) ansätze and its linearized coupled cluster (pCCD-LCC) corrections using the canonical Hartree-Fock and pCCD-optimized (localized) orbital bases. The accuracy of pCCD-based dipole moments is assessed against experimental and CCSD(T) reference values using relaxed and unrelaxed density matrices and different basis set sizes. Our test set comprises molecules of various bonding patterns and electronic structures, exposing pCCD-based methods to a wide range of electron correlation effects. Additionally, we investigate the performance of pCCD-in-DFT dipole moments of some model complexes. Finally, our work indicates the importance of orbital relaxation in the pCCD model and shows the limitations of the linearized couple cluster corrections in predicting electronic dipole moments of multiple-bonded systems. Most importantly, pCCD with a linearized CCD correction can reproduce the dipole moment surfaces in singly bonded molecules, which are comparable to the multireference ones.

Quantification of Stern Layer Water Molecules, Total Potentials, and Energy Densities at Fused Silica:Water Interfaces for Adsorbed Alkali Chlorides, CTAB, PFOA, and PFAS

We have employed amplitude- and phase-resolved second-harmonic generation spectroscopy to investigate ion-specific effects of monovalent cations at the fused silica:water interface maintained under acidic, neutral, and alkaline conditions. We find a negligible dependence of the total potential (as negative as -400 mV at pH 14), the second-order nonlinear susceptibility (as large as 1.5 × 10-21 m2 V-1 at pH 14), the number of Stern layer water molecules (1 × 1015 cm-2 at pH 5.8), and the energy associated with water alignment upon going from neutral to high pH (ca. -24 kJ mol-1 to -48 kJ mol-1 at pH 13 and 14, close to the cohesive energy of liquid water but smaller than that of ice) on chlorides of the alkali series (M+ = Li+, Na+, K+, Rb+, and Cs+). Attempts are presented to provide estimates for the molecular hyperpolarizability of the cations and anions in the Stern layer at high pH, which arrive at ca. 20-fold larger values for αtotal ions(2) = αM+(2) + αOH-(2) + αCl-(2) when compared to water's molecular hyperpolarizability estimate from theory and point to a sizable contribution of deprotonated silanol groups at high pH. In contrast to the alkali series, a pronounced dependence of the total potential and the second-order nonlinear susceptibility on monovalent cationic (cetrimonium bromide, CTAB) and anionic (perfluorooctanoic and perfluorooctanesulfonic acid, PFOA and PFOS) surfactants was quantifiable. Our findings are consistent with a low surface coverage of the alkali cations and a high surface coverage of the surfactants. Moreover, they underscore the important contribution of Stern layer water molecules to the total potential and second-order nonlinear susceptibility. Finally, they demonstrate the applicability of heterodyne-detected second-harmonic generation spectroscopy for identifying perfluorinated acids at mineral:water interfaces.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

Calculation of absolute Raman scattering cross-sections using vibrational self-consistent field/vibrational configuration interaction wave functions

In the present study, the differential scattering cross-sections, depolarization ratios and Raman shifts of small molecular systems are obtained from configuration iteration wave functions of vibrational self-consistent field (VSCF) states. The transition polarizabilities were modeled using the Placzek approximation, neglecting those contributions not arising from the electric dipole mechanism. This theoretical approach is considered a good approximation for samples that absorb in the UV range if the excitation radiation falls in the visible region, as is the case of the molecules selected for the present study, namely: water, methane, and acetylene. Potential energy and electronic polarizability surfaces are calculated by the CCSD(T) and CC3 methods with aug-cc-p(C)V(T,Q,5)Z basis sets. The vibrational Hamiltonian includes the vibrational angular momentum contribution of the Watson kinetic energy operator. As expected, due to the variational nature of the VSCF and vibrational configuration interaction (VCI) methods, the Raman transition wavenumbers are substantially improved over the harmonic predictions. Surprisingly, the scattering cross-sections obtained using the harmonic approximation or the VSCF method better agrees with the experimental values than those cross-sections predicted using VCI wave functions. The more significant deviations of the VCI results from the experimental reference may be related to the significant uncertainties of the measured cross-sections. Still, it may also indicate that the VCI Raman transition moments may require a more accurate description of the electronic polarizability surface. Finally, the depolarization ratios calculated for H₂ O and C₂ D₂ using harmonic and VCI wave functions have similar accuracy, whereas, for C₂ H₂ and C₂ HD, the VCI results are more accurate.

Why local and non-local terms are essential for second harmonic generation simulation?

Second Harmonic Generation (SHG) today represents one of the most powerful techniques to selectively probe all types of interfaces. However, the origin of the SHG signal at a molecular level is still debated since the local dipole contribution, which is strongly correlated to the molecular orientation can be counterbalanced by non-local quadrupole contributions. Here, we propose a method to simulate the SHG signal of a model water/air interface from the molecular response of each contribution. This method includes both local and non-local terms, which are represented, respectively, by the dependency of the polarisability and hyperpolarisability upon the chemical environment of the molecule and by the bulk quadrupole response. The importance of both terms for the sound simulation of the SHG signals and their interpretation is assessed. We demonstrate that the sole dipole term is unable to simulate a SHG signal, even if the dependency of the hyperpolarisability on the local environment is considered. The inclusion of the bulk quadrupole contribution, which largely dominates the dipole contribution, is essential to predict the SHG response, although the accuracy of the prediction is increased when the dependency upon the local environment is considered.

Long-Range Orientational Organization of Dipolar and Steric Liquids

Long-range orientational correlations in liquids have received recent renewed interest, in particular for the neat water case. These long-range orientational correlations, exceeding several tens of nanometers, originate from the presence of the strong permanent water dipolar moment. However, the exact dependence with the dipolar moment and the role of other local forces like steric hindrance has never been addressed. In this work, we experimentally measure long-range correlations for a set of liquids differing by their molecular weight and dipolar moment, in order to reveal the origin of their long-range organization. Hence, we show that the dipolar moment of a solvent molecule is not the unique feature determining the orientational correlation. Steric hindrance significantly helps to structure the liquids as well. In order to quantify these long-range correlations, we also derive theoretically the polarization resolved second harmonic scattering intensity as a function of the rotational invariants describing the dipolar and octupolar interaction.

Computational study of polarizability anisotropies

The dipole polarizabilities (α) and polarizability anisotropies (Δα) of over 20 molecules are calculated to search for negative Δα. The geometry of each molecule is first optimized at the level of CCSD(T)/cc-pVQZ. Then, the α tensors are computed both with CCSD(T)/daug-cc-pVTZ in Gaussian 09 and with the exchange-correlation potential Vxc known as SAOP in the Amsterdam density functional theory program called ADF and a large basis set called QZ3P-3DIFFUSE. In addition to the popular formula of the ΔαRaman connected with Raman spectroscopy, we also present values of an alternative definition of the polarizability anisotropy ΔαKerr connected with Kerr spectroscopy, recently proposed by Kampfrath and colleagues (2018. Chem. Phys. Lett. 692: 319). On one hand, the signs of many ΔαRaman are undetermined; on the other hand, we obtain negative ΔαKerr for more than one-half of the small molecules studied. Of the 24 molecules studied, 18 have negative ΔαKerr.

Molecular structure, second- and third-order nonlinear optical properties and DFT studies of a novel non-centrosymmetric chalcone derivative: (2E)-3-(4-fluorophenyl)-1-(4-{[(1E)-(4-fluorophenyl)methylene]amino}phenyl)prop-2-en-1-one

In the present work, the title chalcone, (2E)-3-(4-fluorophenyl)-1-(4-{[(1E)-(4-fluorophenyl) methylene]amino}phenyl)prop-2-en-1-one (abbreviated as FAMFC), was synthesized and structurally characterized by single-crystal X-ray diffraction. The compound is crystallized in the monoclinic system with non-centrosymmetric space group P2₁ and hence it satisfies the essential condition for materials to exhibit second-order nonlinear optical properties. The molecular structure was further confirmed by using FT-IR and ¹H NMR spectroscopic techniques. The title crystal is transparent in the Vis-NIR region and has a direct band gap. The third-order nonlinear optical properties were investigated in solution (0.01M) by Z-scan technique using a continuous wave (CW) DPSS laser at the wavelength of 532nm. The title chalcone exhibited significant two-photon absorption (β=35.8×10^-5cmW^-1), negative nonlinear refraction (n₂=-0.18×10^-8cm²W^-1) and optical limiting (OL threshold=2.73kJcm^-2) under the CW regime. In support of the experimental results, a comprehensive theoretical study was carried out on the molecule of FAMFC using density functional theory (DFT). The optimized geometries and frontier molecular orbitals were calculated by employing B3LYP/6-31+G level of theory. The optimized molecular structure was confirmed computationally by IR vibrational and ¹H NMR spectral analysis. The experimental UV-Vis-NIR spectrum was interpreted using computational chemistry under time-dependent DFT. The static and dynamic NLO properties such as dipole moments (μ), polarizability (α), and first hyperpolarizabilities (β) were computed by using finite field method. The obtained dynamic first hyperpolarizability β(-2ω;ω,ω) at input frequency ω=0.04282a.u. is predicted to be 161 times higher than urea standard. The electronic excitation energies and HOMO-LUMO band gap for FAMFC were also evaluated by DFT. The experimental and theoretical results are in good agreement, and the NLO study suggests that FAMFC molecule can be a potential candidate in the nonlinear optical applications.

Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode

The Pockels effect of polar organic solvents and water within the electric double layer on an ITO electrode is studied to find that water has the largest Pockels coefficient, followed in order by methanol, ethanol, and dimethyl sulfoxide.

Polarization response of clathrate hydrates capsulated with guest molecules

Clathrate hydrates are characterized by their water cages encapsulating various guest atoms or molecules. The polarization effect of these guest-cage complexes was studied with combined density functional theory and finite-field calculations. An addition rule was noted for these systems whose total polarizability is approximately equal to the polarizability sum of the guest and the cage. However, their distributional polarizability computed with Hirshfeld partitioning scheme indicates that the guest-cage interaction has considerable influence on their polarization response. The polarization of encapsulated guest is reduced while the polarization of water cage is enhanced. The counteraction of these two opposite effects leads to the almost unchanged total polarizability. Further analysis reveals that the reduced polarizability of encapsulated guest results from the shielding effect of water cage against the external field and the enhanced polarizability of water cage from the enhanced bonding of hydrogen bonds among water molecules. Although the charge transfer through the hydrogen bonds is rather small in the water cage, the polarization response of clathrate hydrates is sensitive to the changes of hydrogen bonding strength. The guest encapsulation strengthens the hydrogen bonding network and leads to enhanced polarizability.

CCSD(T) calculations of confined systems: in-crystal polarizabilities of F⁻, Cl⁻, O²⁻, and S²⁻

We explore dipole polarizabilities of the singly and doubly charged anions F(-), Cl(-), O(2-), and S(2-) in an external, harmonic oscillator (HO) confining potential ∑(i)½ω(2)r(i)(2). We find that in contrast to F(-) and Cl(-) those for O(2-) and S(2-) are unrealistically high due to the instability of the corresponding restricted Hartree-Fock (RHF) solutions. Yet, already a relatively weak HO confining potential stabilizes their RHF solutions and eliminates any possible broken-symmetry solutions. The coupled-cluster theory with single, double and noniterative triple excitations (CCSD(T)) then yields considerably reduced polarizabilities for O(2-) and S(2-) relative to their unconfined values. We showed that polarizabilities of O(2-) and S(2-) are more sensitive to the strength of a confinement potential than are those for F(-) and Cl(-). This enables us to relate the confining parameter ω with the known experimental polarizabilities for selected crystals (our "training set") and to find a specific confining parameter ω for which the CCSD(T) polarizability equals the experimental in-crystal polarizability of an anion in the training set. The latter may then be used as an alternative approach for determining the in-crystal polarizabilities of anions by exploiting the fact that the characteristic ω values depend linearly on the ionic radius of a cation participating in specific crystals containing these anions. Using this method we then calculate the isotropic dipole polarizabilities for F(-), Cl(-), O(2-), and S(2-) embedded in the LiF, LiCl, NaF, NaCl, KF, KCl, ZnO, ZnS, MgO, MgS, CaO, CaS, SrO, SrS, BaO, BaS, and other crystals containing halogen, oxygen, or sulphur anions. We compare our results with those obtained via alternative models of the in-crystal anionic polarizabilities.

One lithium atom binding with P-nitroaniline: lithium salts or lithium electrides?

Recently, both lithium (Li) salts and Li electrides formed by one Li atom interacting with ligand complexes, have been widely investigated. An interesting question emerges: is the configuration of one Li atom interacting with ligand complexes a Li salt or electride? In the present work, four configurations n-Li-PNA (n = 1-4) were obtained by binding one Li atom with the p-nitroaniline (PNA) at different positions to explore this question. The results show that 1-Li-PNA and 2-Li-PNA are typical Li salts, and 4-Li-PNA is a typical Li electride. Significantly, 3-Li-PNA possesses both characteristics of Li salt and electride. At the same time, 3-Li-PNA has the largest first hyperpolarizability (2.9 × 10(6) au) by ROMP2 method compared with the other three configurations. Furthermore, the first hyperpolarizability of 3-Li-PNA is about 2600 times larger than that of PNA. Further, the vertical ionization potential (VIP) and interaction energy (E int) indicate that 3-Li-PNA is less stable than 1-Li-PNA and 2-Li-PNA (Li salts), but is more stable than 4-Li-PNA (Li electrides).

Polarizability series of aqueous polyatomic anions revealed by femtosecond Kerr effect spectroscopy

Femtosecond OHD-RIKES measurements show that the hyperpolarizability series of aqueous polyatomic anions increases in the following sequence HPO₄²⁻ < HSO₄⁻ < CO₃²⁻ < AC⁻ < NO₃⁻ < SCN⁻.

Intermolecular polarizability dynamics of aqueous formamide liquid mixtures studied by molecular dynamics simulations

A molecular dynamics simulation study is presented for the relaxation of the polarizability anisotropy in liquid mixtures of formamide and water, using a dipolar induction scheme that involves the intrinsic polarizability and first hyperpolarizability tensors of the molecules, and the dipole-quadrupole polarizability of water species. The long time diffusive decay of the collective polarizability anisotropy correlations exhibits a substantial slowing down as the formamide mole fraction increases in the mixture. The diffusive times for the polarizability relaxation obtained from the authors' simulations are in good agreement with optical Kerr effect experimental data, and they are found to correlate nearly linearly with the estimated mean lifetimes of the hydrogen bonds within the mixture, suggesting that the relaxation of the hydrogen bond network is responsible to some extent for the collective relaxation of the polarizability anisotropy of the mixture. The short time behavior of the polarizability anisotropy relaxation was investigated by computing the nuclear response function, R(t), which is very rapidly dominated by the formamide contribution as it is added to water, due to the much larger polarizability anisotropy of formamide molecules compared to that of water. Several contributions to the Raman spectrum were also analyzed as a function of composition, and the dynamical origin of the different bands was determined.

Ab initiodipole polarizability surfaces of water molecule: Static and dynamic at 514.5nm

Coupled cluster calculations with a carefully designed basis set have been performed to obtain both static, alpha, and dynamic at 514.5 nm, alpha(514.5 nm), dipole polarizability surfaces of water. We employed a medium size basis set (13s10p6d3f9s6p2d1f)[9s7p6d3f6s5p2d1f] consisting of 157 contracted Gaussian-type functions that yields values near the Hartree-Fock limit for alpha [G. Maroulis, J. Chem. Phys. 94, 1182 (1991)]. The alpha and alpha(514.5 nm) surfaces were able to reproduce all the experimentally available information about the dipole polarizability of water, especially the Raman spectra of gaseous H(2)O, D(2)O, and HDO. Vibrational averages for the dipole polarizability of water molecule are also reported.

Charge-on-spring polarizable water models revisited: From water clusters to liquid water to ice

The properties of two improved versions of charge-on-spring (COS) polarizable water models (COS/G2 and COS/G3) that explicitly include nonadditive polarization effects are reported. In COS models, the polarization is represented via a self-consistently induced dipole moment consisting of a pair of separated charges. A previous polarizable water model (COS/B2), upon which the improved versions are based, was developed by Yu, Hansson, and van Gunsteren. To improve the COS/B2 model, which overestimated the dielectric permittivity, one additional virtual atomic site was used to reproduce the water monomer quadrupole moments besides the water monomer dipole moment in the gas phase. The molecular polarizability, residing on the virtual atomic site, and Lennard-Jones parameters for oxygen-oxygen interactions were varied to reproduce the experimental values for the heat of vaporization and the density of liquid water at room temperature and pressure. The improved models were used to study the properties of liquid water at various thermodynamic states as well as gaseous water clusters and ice. Overall, good agreement is obtained between simulated properties and those derived from experiments and ab initio calculations. The COS/G2 and COS/G3 models may serve as simple, classical, rigid, polarizable water models for the study of organic solutes and biopolymers. Due to its simplicity, COS type of polarization can straightforwardly be used to introduce explicit polarization into (bio)molecular force fields.

Ab initio determination of the electric multipole moments and static (hyper)polarizability of HCCX, X = F, Cl, Br, and I

We report electric multipole moments and (hyper)polarizabilities for the haloethynes HCCX, X = F, Cl, Br, and I. The molecular properties have been obtained from finite-field self-consistent field, Møller-Plesset perturbation theory and coupled cluster calculations with large, carefully optimized basis sets of gaussian-type functions. The mean dipole (hyper)polarizability and the mean quadrupole polarizability near the Hartree-Fock limit are alpha/e(2)a(0) (2)E(h) (-1) = 23.74 (HCCF), 37.26 (HCCCl), 43.97 (HCCBr), 56.44 (HCCI), beta/e(3)a(0) (3)E(h) (-2) = -73.9 (HCCF), -67.0 (HCCCl), -39.5 (HCCBr), 42.7 (HCCI), gamma/e(4)a(0) (4)E(h) (-3) = 4,914 (HCCF), 6,554 (HCCCl), 9,328 (HCCBr), 14,949 (HCCI), and C/e(2)a(0) (4)E(h) (-1) = 160.3 (HCCF), 317.1 (HCCCl), 471.2 (HCCBr), 671.2 (HCCI). Electron correlation has a small effect on the dipole polarizability but affects strongly the hyperpolarizability. Agreement with the available experimental data is more or less fair for HCCF, HCCCl, and HCCBr but less satisfactory for HCCI.