Coupled-Cluster Based Linear Response Approach to Property Calculations: Dynamic Polarizability and Its Static Limit

Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory

With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438-5447], the fourth-order Runge-Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.

A Fock space coupled cluster based probing of the single- and double-ionization profiles for the poly-cyclic aromatic hydrocarbons and conjugated polyenes

Sequential formation of a poly-cyclic aromatic hydrocarbon (PAH) dication in the H I regions of the interstellar medium (ISM) is proposed to be a function of internal energy of the doubly ionized PAHs, which, in turn, is dependent on the single- and double-ionization potentials of the system. This sets a limit on the single- and double-ionization energies of the system(s) that can further undergo sequential absorption of two photons, leading to a dication (PAH⁺²). Here, we report the single-ionization (I⁺¹) and double-ionization (I⁺²) energies and the I⁺²/I⁺¹ ratio for some selected PAHs and conjugated polyenes obtained using the Fock space coupled cluster technique, enabling simultaneous consideration of several electronic states of different characters. The I⁺² to I⁺¹ ratio bears a constant ratio, giving allowance to determine I⁺² from the knowledge of single-ionization (I⁺¹) and vice versa. Our observations are in good agreement with the established literature findings, confirming the reliability of our estimates. The measured single- and double-ionization energies further demonstrate that the sequential formation and fragmentation of a PAH dication in the H I regions of the ISM for systems such as benzene and conjugated polyenes such as ethylene and butadiene are quite unlikely because I⁺²-I⁺¹ for such system(s) is higher than the available photon energy in the H I regions of the ISM. Present findings may be useful to understand the formation and underlying decay mechanisms of multiply charged ions from PAHs and related compounds that may accentuate the exploration of the phenomenon of high-temperature superconductivity.

Single-Root Multireference Brillouin-Wigner Perturbative Approach to Excitation Energies

The state-specific Brillouin-Wigner multireference perturbation theory [which employs Jeziorski-Monkhorst parametrization of the wave function] using improved virtual orbitals, denoted as IVO-BWMRPT, is applied to calculate excitation energies (EEs) for methylene, ethylene, trimethylenemethane, and benzyne systems exhibiting various degrees of diradical character. In IVO-BWMRPT, all of the parameters appearing in the wave function ansatz are optimized for a specific electronic state. For these systems, the IVO-BWMRPT method provides EEs that are in close agreement with the benchmark results and experiments, where available, indicating that the method does not introduce imbalance in the target-specific treatment of closed- and open-shell states involved. The good performance of the present methodology is primarily related to structural compactness of the formalism. Overall, present findings are encouraging for both further development of the approach and chemical applications on the energy differences of strongly correlated systems.

On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions

In this work, we investigate how geometric changes influence the static dipole polarizability (α) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C ₆ dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H₂O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic (α _iso) and nearly 50% to the anisotropic (α _aniso) polarizability values. In doing so, we find that α _iso = 9.8307 bohr³, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr³ provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

A confinement induced spectroscopic study of noble gas atoms using equation of motion architecture: Encapsulation within fullerene's voids

A relativistic study of spectroscopic properties of the endohedral fullerenes Ng@C₆₀^q (where Ng = He, Ne and q=0,±1,±2 are the charges) associated with the C₆₀ molecule has been done using the equation of motion coupled cluster (EOM-CC) methodology. Specific properties estimated are the transition energies, dipole oscillator strengths, and transition probabilities for the low-lying excitations 1s²(¹S₀) → 1snp (¹P₁) (n = 2, 3, 4) for He@C₆₀^q and 1s²2s²2p⁶ (¹S₀) → 1s²2s²2p⁵ns∕nd (¹P₁) (n = 3, 4) for Ne@C₆₀^q, which have been compared with those for the isolated atom to depict the confinement effect of the host molecule on the encapsulated atom. This is accomplished by introducing an effective potential to the atomic Hamiltonian induced by the fullerene moiety and its charge. The EOM-CC results have been compared with those estimated with the random phase approximation (and configuration interaction singles) to understand the effect of electron correlation under such confinement. The systematic and interesting behavior of the properties is highlighted indicating the effect of fullerene cage potential on the redistribution of electron density of the guest atom.

Coupled-cluster sum-frequency generation nonlinear susceptibilities of methyl (CH3) and methylene (CH2) groups

The first vibrational sum frequency generation (SFG) spectra based on molecular properties calculated at the coupled cluster singles and doubles (CCSD) level of approximation have been simulated for interfacial model alkyl chains, providing benchmark data for comparisons with approximate methods, including density functional theory (DFT). The approach proceeds in three steps. In the first two steps, the molecular spectral properties are determined: the vibrational normal modes and frequencies and then the derivatives of the dipole moment and of the polarizability with respect to the normal coordinates. These derivatives are evaluated with a numerical differentiation approach, of which the accuracy was monitored using Romberg's procedure. Then, in the last step, a three-layer model is employed to evaluate the macroscopic second-order nonlinear optical responses and thereby the simulated SFG spectra of the alkyl interface. Results emphasize the following facts: (i) the dipole and polarizability derivatives calculated at the DFT level with the B3LYP exchange-correlation functional can differ, with respect to CCSD, by as much as ±10 to 20% and ±20 to 50% for the CH₃ and CH₂ vibrations, respectively; (ii) these differences are enhanced when considering the SFG intensities as well as their variations as a function of the experimental configuration (ppp versus ssp) and as a function of the tilt and rotation angles, defining the orientation of the alkyl chain at the interface; (iii) these differences originate from both the vibrational normal coordinates and the Cartesian derivatives of the dipole moment and polarizability; (iv) freezing the successive fragments of the alkyl chain strongly modifies the SFG spectrum and enables highlighting the delocalization effects between the terminal CH₃ group and its neighboring CH₂ units; and finally (v) going from the free chain to the free methyl model, and further to C_3v constraints on leads to large variations of two ratios that are frequently used to probe the molecular orientation at the interface, the (r + r)/r⁺ ratio for both antisymmetric and symmetric CH₃ vibrations and the I_ppp/I_ssp ratio.

Reappraisal of nuclear quadrupole moments of atomic halogens via relativistic coupled cluster linear response theory for the ionization process

The coupled cluster based linear response theory (CCLRT) with four-component relativistic spinors is employed to compute the electric field gradients (EFG) of (35)Cl, (79)Br, and (127)I nuclei. The EFGs resulting from these calculations are combined with experimental nuclear quadrupole coupling constants (NQCC) to determine the nuclear quadrupole moments (NQM), Q of the halide nuclei. Our estimated NQMs [(35)Cl = -81.12 mb, (79)Br = 307.98 mb, and (127)I = -688.22 mb] agree well with the new atomic values [(35)Cl = -81.1(1.2), (79)Br = 302(5), and (127)I = -680(10) mb] obtained via Fock space multireference coupled cluster method with the Dirac-Coulomb-Breit Hamiltonian. Although our estimated Q((79)Br) value deviates from the accepted reference value of 313(3) mb, it agrees well with the recently recommended value, Q((79)Br) = 308.7(20) mb. Good agreement with current reference data indicates the accuracy of the proposed value for these halogen nuclei and lends credence to the results obtained via CCLRT approach. The electron affinities yielded by this method with no extra cost are also in good agreement with experimental values, which bolster our belief that the NQMs values for halogen nuclei derived here are reliable.

A Comparison of Møller-Plesset and Coupled Cluster Linear Response Theory Methods for the Calculation of Dipole Oscillator Strength Sum Rules and C6 Dispersion Coefficients

Four correlated linear response theory methods - the second order polarization propagator approximation (SOPPA), the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes, SOPPA(CCSD), the CC2 and coupled cluster singles doubles (CCSD) linear response theory - were used to determine the dipole oscillator strength sum rules of the hydrogen halides HX (with X = F, Cl, Br and I) and the C6 dispersion coefficient for all pairs of interacting HX molecules via numerical integration of the Casimir-Polder formula. The dependence of the polarizabilities, their frequency dependence and the C6 coefficients on the level of correlation and the dependence of the C6 coefficients on the two intramolecular bond lengths were studied.

Explicitly intruder-free valence-universal multireference coupled cluster theory as applied to ionization spectroscopy

Although it is quite promising to compute the spectroscopic energies [say, ionization potential (IP)] via the traditional valence-universal multireference coupled cluster (VUMRCC) method based on the description of the complete model space being seriously plagued by the perennial intruder state problem, the eigenvalue independent partitioning (EIP) based VUMRCC (coined as EIP-MRCC) method is quite effective to predict the spectroscopic energies in an intruder-free manner. Hence, the EIP-MRCC method is suitable for generating both the principal IPs and the satellite IPs of the inner-valence region. An EIP strategy converts the nonlinear VUMRCC equations for M(m,n) dimensional model space of m hole and n particle to a non-Hermitian eigenproblem of larger dimension whose M(m,n) roots are only physically meaningful. To increase the quality of the computed energy differences in the sense of chemical accuracy and to locate the correct position of it in the spectrum, the inclusion of higher-body cluster operators on top of all the standard singles-doubles is not the only pivotal issue, the effect of the size of the basis set is also equally important. This paper illustrates these issues by calculating the principal and satellite IPs of HF and HCl molecules using various basis sets (viz., Dunning's cc-pVDZ, cc-pVTZ, and cc-pVQZ) via EIP-MRCC method with full inclusion of triples (abbreviated as EIP-MRCCSDT). The results seem quite encouraging in comparison with the experimental values. The controversial 2Pi satellite at 28.67 eV of HCl of Svensson et al. [J. Chem. Phys. 89, 7193 (1988)] is also reported.

Direct Formation of Ge−C Bonds from GeO2

Germanium dioxide in the presence of 5% KOH reacted with dimethyl carbonate (DMC) at 250 degrees C to give (MeO)(4)Ge. The reaction of GeO(2) and DMC is similar to that reported for SiO(2); however, the rate of reaction for germanium is much higher than that of the corresponding silicon reaction. In a side-by-side experiment using SiO(2) and GeO(2) where the surface area of the silicon dioxide was 2 orders of magnitude higher than that of the GeO(2), the base-catalyzed reaction with DMC was about an order of magnitude higher for the germanium dioxide. When GeO(2) and 5% KOH were reacted with DMC at 350 degrees C, two products formed: (MeO)(4)Ge (70%) and MeGe(OMe)(3) (30%). Confirmation of the identity of MeGe(OMe)(3) was by GCMS, (1)H and (13)C NMR, and comparison to an authentic sample made by reaction of MeGeCl(3) with NaOMe. Experiments to determine the mechanism of the direct formation of Ge-C from GeO(2) ruled out participation from CO, H(2), or carbon. The KOH-catalyzed reaction of other metal oxides was explored including B(2)O(3), Ga(2)O(3), TiO(2), Sb(2)O(3), SnO(2), and SnO. Boron reacted to give unknown volatile products. Antimony reacted to give a solid which analyzed as Sb(OMe)(3). SnO reacted with DMC to give a mixture that included (MeO)(4)Sn and possibly Me(3)Sn(OMe).