Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Erratum: "The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization" [J. Chem Phys. 122, 014109 (2005)]

An erratum to the article "The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization", published in The Journal Chemistry of Physics, 2005, v.122, art. no.014109. Values FLU have been corrected in the last column of Table I because they were not correct

The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization

In this work, the aromatic fluctuation index (FLU) that describes the fluctuation of electronic charge between adjacent atoms in a given ring is introduced as a new aromaticity measure. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized circulation of π electrons. It is defined not only considering the amount of electron sharing between contiguous atoms, which should be substantial in aromatic molecules, but also taking into account the similarity of electron sharing between adjacent atoms. For a series of rings in 15 planar polycyclic aromatic hydrocarbons, we have found that, in general, FLU is strongly correlated with other widely used indicators of local aromaticity, such as the harmonic-oscillator model of aromaticity, the nucleus independent chemical shift, and the para-delocalization index (PDI). In contrast to PDI, the FLU index can be applied to study the aromaticity of rings with any number of members and it can be used to analyze both the local and global aromatic character of rings and molecules

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems

The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

One- and two-center energy components in the atoms in molecules theory

The energy decomposition scheme proposed in a recent paper has been realized by performing numerical integrations. The sample calculations carried out for some simple molecules show excellent agreement with the chemical picture of molecules, indicating that such an energy decomposition analysis can be useful from the point of view of connecting quantum mechanics with the genuine chemical concepts

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone